**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
import java.util.*;
import java.io.*;
public class E {
    static FastReader in = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) {
        int tc = in.nextInt();
        for(int z=0; z<tc; ++z){
            int n = in.nextInt();
            long[] a = new long[n], b = new long[n];
            for(int i=0; i<n; ++i){
                a[i] = in.nextInt();
                b[i] = in.nextInt();
            }
            long[] t = new long[n];
            t[0] = a[0];
            SegmentTree seg = new SegmentTree(t);
            HashMap<Long,Integer> lastIndex = new HashMap<>();
            lastIndex.put(b[0],0);
            out.print(t[0]+" ");
            for(int i=1; i<n; ++i){
                if(lastIndex.containsKey(b[i])){
                    int j = lastIndex.get(b[i]);
                    long between = seg.get(j+1,i-1);
                    if(between>=t[j] || between>=a[i]){
                        t[i] = a[i];
                    }
                    else{
                        t[i] = between+a[i]-between+(t[j]-between);
                    }
                }
                else{
                    t[i] = a[i];
                }
                seg.set(i,t[i]);
                out.print(seg.get(0,i)+" ");
                lastIndex.put(b[i],i);
            }
            out.println();
        }
        out.flush();
    }
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    String nextLine() {
        String str = "";
        try {
            if(st.hasMoreTokens()){
                str = st.nextToken("\n");
            }
            else{
                str = br.readLine();
            }
        }
        catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
class SegmentTree{
    long[] tree;
    static long none = Long.MIN_VALUE;
    private long operation(long a, long b){
        return a>b ? a : b;
    }
    public SegmentTree(long[] a){
        int leaves=a.length;
        if((leaves&(leaves-1))!=0){
            int log=-1;
            while(leaves>0){
                leaves>>=1;
                log++;
            }
            leaves=1<<(log+1);
        }
        tree= new long[2*leaves-1];
        for(int i=0; i<a.length; ++i) tree[i+leaves-1]=a[i];
        for(int i=leaves-2; i>=0; --i) tree[i]=operation(tree[2*i+1],tree[2*i+2]);
    }
    private long get(int l, int r, int x,int lx, int rx){
        if(lx>=l && rx<=r) return tree[x];
        if(rx < l || lx > r) return none;
        return operation(get(l,r,2*x+1,lx,(rx+lx)/2),get(l,r,2*x+2,(rx+lx)/2+1,rx));
    }
    public long get(int l, int r){
        return get(l,r,0,0,tree.length/2);
    }
    public void set(int i, long x){
        tree[i+tree.length/2]=x;
        i+=tree.length/2;
        while(i>0){
            i=(i-1)/2;
            tree[i]=operation(tree[2*i+1],tree[2*i+2]);
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
3
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
import java.util.*;
import java.io.*;
public class E {
    static FastReader in = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) {
        int tc = in.nextInt();
        for(int z=0; z<tc; ++z){
            int n = in.nextInt();
            int[] a = new int[n], b = new int[n];
            for(int i=0; i<n; ++i){
                a[i] = in.nextInt();
                b[i] = in.nextInt();
            }
            long[] t = new long[n];
            t[0] = a[0];
            SegmentTree seg = new SegmentTree(t);
            HashMap<Integer,Integer> lastIndex = new HashMap<>();
            lastIndex.put(b[0],0);
            out.print(t[0]+" ");
            for(int i=1; i<n; ++i){
                if(lastIndex.containsKey(b[i])){
                    int j = lastIndex.get(b[i]);
                    long between = seg.get(j+1,i-1);
                    if(between>=t[j] || between>=a[i]){
                        t[i] = a[i];
                    }
                    else{
                        t[i] = between+a[i]-between+(t[j]-between);
                    }
                }
                else{
                    t[i] = a[i];
                }
                seg.set(i,t[i]);
                out.print(seg.get(0,i)+" ");
                lastIndex.put(b[i],i);
            }
            out.println();
        }
        out.flush();
    }
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    String nextLine() {
        String str = "";
        try {
            if(st.hasMoreTokens()){
                str = st.nextToken("\n");
            }
            else{
                str = br.readLine();
            }
        }
        catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
class SegmentTree{
    long[] tree;
    static long none = Long.MIN_VALUE;
    private long operation(long a, long b){
        return a>b ? a : b;
    }
    public SegmentTree(long[] a){
        int leaves=a.length;
        if((leaves&(leaves-1))!=0){
            int log=-1;
            while(leaves>0){
                leaves>>=1;
                log++;
            }
            leaves=1<<(log+1);
        }
        tree= new long[2*leaves-1];
        for(int i=0; i<a.length; ++i) tree[i+leaves-1]=a[i];
        for(int i=leaves-2; i>=0; --i) tree[i]=operation(tree[2*i+1],tree[2*i+2]);
    }
    private long get(int l, int r, int x,int lx, int rx){
        if(lx>=l && rx<=r) return tree[x];
        if(rx < l || lx > r) return none;
        return operation(get(l,r,2*x+1,lx,(rx+lx)/2),get(l,r,2*x+2,(rx+lx)/2+1,rx));
    }
    public long get(int l, int r){
        return get(l,r,0,0,tree.length/2);
    }
    public void set(int i, long x){
        tree[i+tree.length/2]=x;
        i+=tree.length/2;
        while(i>0){
            i=(i-1)/2;
            tree[i]=operation(tree[2*i+1],tree[2*i+2]);
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5
1 0
1 1
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
#include <bits/stdc++.h>
using ll = long long;
int main()
{
    int T;
    std::cin >> T;
    while (T--) {
        int n;
        std::cin >> n;
        std::vector<ll> a(n + 1), b(n + 1);
        for (int i = 1; i <= n; i++) {
            std::cin >> a[i] >> b[i];
        }
        std::vector<ll> stk(n + 1);
        int p = 0, remain = 0;
        for (int i = 1; i <= n; i++) {
            while (p) {
                if (b[stk[p]] != b[i]) {
                    if (a[stk[p]] <= a[i]) remain = a[stk[p]], p--;
                    else break;
                } else {
                    a[i] += a[stk[p]] - remain;
                    p--;
                    remain = 0;
                }

            }
            stk[++p] = i;
            std::cout << a[stk[1]] << ' ';
        }
        std::cout << '\n';
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
3
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
#include <bits/stdc++.h>

using namespace std;

#ifdef lisie_bimbi
#else
#define endl '\n'
#endif
typedef long long ll;

const int inf = 1'000'000'000;

struct segment_tree {
    vector<ll> st;
    int sz;
    segment_tree(int n) {
        sz = 1;
        while (sz < n) {
            sz *= 2;
        }
        st.resize(2 * sz, 0);
    }
    void set(int i, int v) {
        i += sz;
        st[i] = v;
        i /= 2;
        while (i) {
            st[i] = max(st[2 * i], st[2 * i + 1]);
            i /= 2;
        }
    }
    ll get(int l, int r) {
        l += sz;
        r += sz;
        ll ans = -2;
        while (l <= r) {
            if (l & 1) {
                ans = max(ans, st[l++]);
            }
            if (~r & 1) {
                ans = max(ans, st[r--]);
            }
            l >>= 1;
            r >>= 1;
        }
        return ans;
    }
};

void solve() {
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i] >> b[i];
    }
    segment_tree st(n + 1);
    vector<vector<pair<ll, ll>>> last(n + 1);
    vector<int> last_upd(n + 1, 0);
    last[b[0]].emplace_back(0, a[0] - 1);
    cout << a[0] << ' ';
    ll ans = a[0];
    for (int i = 1; i < n; i++) {
        int upd = st.get(last_upd[b[i]] + 1, i - 1);
        while (!last[b[i]].empty() && last[b[i]].back().first <= upd) {
            last[b[i]].back().first = upd + 1;
            if (last[b[i]].back().first > last[b[i]].back().second) {
                last[b[i]].pop_back();
            }
        }
        ll nw = a[i] - 1;
        while (!last[b[i]].empty() && nw >= last[b[i]].back().first - 1) {
            nw += last[b[i]].back().second - last[b[i]].back().first + 1;
            last[b[i]].pop_back();
        }
        last[b[i]].emplace_back(0, nw);
        last_upd[b[i]] = i;
        st.set(i, nw);
        ans = max(ans, nw + 1);
        cout << ans << ' ';
    }
    cout << '\n';
}

int32_t main() {
#ifdef lisie_bimbi
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#else
    cin.tie(nullptr)->sync_with_stdio(false);
#endif
    int t = 1;
    cin >> t;
    while(t--) {
        solve();
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
4
2 0
1 1
3 0
5 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
for _ in range(int(input())):
	s,x = [(-1,-1)],0
	for __ in range(int(input())):
		a,b = map(int,input().split())
		while s[-1][0] <= a or s[-1][1] == b:
			if s[-1][1] == b: a += s.pop()[0]-x
			elif s[-1][1] == -1: break
			else: x = s.pop()[0]
		s.append((a,b))
		print(s[1][0], end = ' ')
	print()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
3
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
for _ in range(int(input())):
    s, out, x = [(-1, -1)], 0, 0
    for __ in range(int(input())):
        a, b = map(int, input().split())
        x = 0  # Reset x at the start of each iteration
        while s[-1][0] <= a:
            if s[-1][1] == b:
                a += s.pop()[0] - x
            elif s[-1][1] == -1:
                break
            else:
                x = s.pop()[0]
        if s[-1][1] == b:
            a += s[-1][0] - x
            s.pop()
        s.append((a, b))
        print(s[1][0], end=' ')
    print()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
3
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
import java.util.*;

public final class e{
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        scanner.nextLine();
        for(int i=0; i<t; i++){
            solve(scanner);
        }
        scanner.close();
    }

    static void solve(Scanner scanner){
        int n = scanner.nextInt();
        long pairs[][] = new long[n][2];
        for(int i=0; i<n; i++){
            pairs[i][0] = scanner.nextLong();
            pairs[i][1] = scanner.nextLong();
        }
        long s = pairs[0][0];
        Stack<long[]> stack = new Stack<>();
        for(long[] p: pairs){
            long last = 0;
            while(stack.isEmpty()==false && stack.peek()[1]!=p[1] && stack.peek()[0]<=p[0]){
                last = stack.pop()[0];
            }
            if(stack.isEmpty() || stack.peek()[1]!=p[1]){
                stack.push(p);
            }else{
                stack.peek()[0] += p[0]-last;
            }
            s = Math.max(s, stack.peek()[0]);
            System.out.print(s+" ");
        }
        System.out.println();
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
3
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Cosmic Rays
time_limit_ms: 2000
memory_limit_mb: 512
Description: Given an array of integers $s_1, s_2, \ldots, s_l$, every second, cosmic rays will cause all $s_i$ such that $i=1$ or $s_i\neq s_{i-1}$ to be deleted simultaneously, and the remaining parts will be concatenated together in order to form the new array $s_1, s_2, \ldots, s_{l'}$.

Define the strength of an array as the number of seconds it takes to become empty.

You are given an array of integers compressed in the form of $n$ pairs that describe the array left to right. Each pair $(a_i,b_i)$ represents $a_i$ copies of $b_i$, i.e. $\underbrace{b_i,b_i,\cdots,b_i}_{a_i\textrm{ times}}$.

For each $i=1,2,\dots,n$, please find the strength of the sequence described by the first $i$ pairs.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le3\cdot10^5$) — the length of sequence $a$.

The next $n$ lines contain two integers each $a_i$, $b_i$ ($1\le a_i\le10^9,0\le b_i\le n$) — the pairs which describe the sequence.

It is guaranteed that the sum of all $n$ does not exceed $3\cdot10^5$.

It is guaranteed that for all $1\le i<n$, $b_i\neq b_{i+1}$ holds.

Output: For each test case, print one line containing $n$ integers — the answer for each prefix of pairs.

Examples:
input:
4
4
2 0
1 1
3 0
5 1
6
4 6
1 3
4 6
4 0
7 6
6 3
7
9 0
7 1
5 0
7 1
9 0
1 1
2 0
10
10 7
4 9
2 2
7 9
2 8
8 5
11 7
15 5
12 7
4 0
output:
2 2 4 5
4 4 7 7 10 10
9 9 9 9 9 9 10
10 10 10 10 10 10 12 15 15 15

Note: In the first test case, for the prefix of length $4$, the changes will be $[0,0,1,0,0,0,1,1,1,1,1]\rightarrow[0,0,0,1,1,1,1]\rightarrow[0,0,1,1,1]\rightarrow[0,1,1]\rightarrow[1]\rightarrow[]$, so the array becomes empty after $5$ seconds.

In the second test case, for the prefix of length $4$, the changes will be $[6,6,6,6,3,6,6,6,6,0,0,0,0]\rightarrow[6,6,6,6,6,6,0,0,0]\rightarrow[6,6,6,6,6,0,0]\rightarrow[6,6,6,6,0]\rightarrow[6,6,6]\rightarrow[6,6]\rightarrow[6]\rightarrow[]$, so the array becomes empty after $7$ seconds.

Buggy Code:
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int testCases = scanner.nextInt();
        while (testCases-- > 0) {
            int size = scanner.nextInt();
            int[] arrayX = new int[size + 1];
            int[] arrayY = new int[size + 1];
            int[] stack = new int[size + 1];

            int idx = 1;
            while (idx <= size) {
                arrayX[idx] = scanner.nextInt();
                arrayY[idx] = scanner.nextInt();
                idx++;
            }

            int maximumValue = 0;
            int stackTop = 0;

            idx = 1;
            while (idx <= size) {
                int currentMax = 0;
                while (stackTop > 0 && (arrayX[stack[stackTop]] <= arrayX[idx] || arrayY[stack[stackTop]] == arrayY[idx])) {
                    if (arrayY[stack[stackTop]] != arrayY[idx]) {
                        currentMax = Math.max(currentMax, arrayX[stack[stackTop]]);
                        stackTop--;
                    } else {
                        arrayX[idx] -= currentMax;
                        currentMax = 0;
                        arrayX[idx] += arrayX[stack[stackTop]];
                        stackTop--;
                    }
                }

                stack[++stackTop] = idx;
                maximumValue = Math.max(maximumValue, arrayX[idx]);
                System.out.print(maximumValue + " ");

                idx++;
            }

            System.out.println();
        }

        scanner.close();
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5
1 0
1 1
1 0
1 1
1 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include <bits/stdc++.h>
using namespace std;

#define ll long long int
#define pb push_back
const ll M=1e9+7;
ll mod(ll x){
    return (x%M + M)%M;
}
ll mul(ll a,ll b){
    return mod(mod(a) * mod(b));
}
ll add(ll a,ll b){
    return mod(mod(a) + mod(b));
}
void seive(ll n){
    bool primes[n+1];
    fill(primes, primes + n + 1, true);
    primes[0] = primes[1] = false;
    for (ll i = 2; i <= n; i++) {
        if (primes[i]) {
            for (ll j = i * 2; j <= n; j += i) {
                primes[j] = false;
            }
        }
    }
}
unsigned ll getFirstSetBit(ll n) { return log2(n & -n) + 1; }
// ll xorr = accumulate(nums.begin(), nums.end(), 0, bit_xor<>());
// n>>j & 1 (to check if the j th bit is set or not)
void solve(){
 int n,k;
 cin>>n>>k;
 string str1,str2;
 cin>>str1;
 cin>>str2;
 while(k--){
    int l,r;
    cin>>l>>r;
    int len = r-l;
    string res1 = str1.substr(l-1,len+1);
    string res2 = str2.substr(l-1,len+1);
    map<char,int>mpp1;
    map<char,int>mpp2;
    set<char>st;
    for(int i=0;i<res1.size();i++){
        mpp1[res1[i]]++;
        mpp2[res2[i]]++;
        st.insert(res1[i]);
        st.insert(res2[i]);
    }
   int ans=0;
  for(auto it : st){
    if(mpp1.find(it)!=mpp1.end() && mpp2.find(it)!=mpp2.end()){
      if(mpp1[it] == mpp2[it]) continue;
      else ans+=(abs(mpp1[it]-mpp2[it]));
    }
    else ans++;
  }
  cout<<ans/2<<endl;
 }
}
int main() {
    #ifndef ONLINE_JUDGE
        freopen("inputf.in", "r", stdin);
        freopen("outputf.in", "w", stdout);
    #endif

    ll t;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To expose the bug in the given code, we need to focus on edge cases and scenarios where the faulty logic might lead to incorrect results. The primary issue in the code is the way it calculates the number of operations needed to make the substrings equal after sorting. Specifically, the code incorrectly handles the differences in character counts between the two substrings.

Here are the steps to create a challenging test input:

1. **Edge Case with Equal Substrings**: Create a case where the substrings are already equal after sorting, which should require 0 operations.
2. **Edge Case with Minimal Changes**: Create a case where only a few characters need to be changed to make the substrings equal after sorting.
3. **Edge Case with Large Differences**: Create a case where the substrings have a large difference in character counts, requiring a significant number of operations.
4. **Edge Case with Repeated Characters**: Create a case where the substrings have repeated characters, which might cause the code to miscalculate the number of operations.

Let's construct a small-scale test input that covers these scenarios:

```plaintext
4
5 2
abcde
edcba
1 5
1 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
8 4
abcdeabc
bcdeabcd
1 8
1 4
5 8
3 6
```

### Explanation:
1. **Test Case 1**:
   - `n = 5`, `q = 2`
   - `a = "abcde"`, `b = "edcba"`
   - Queries: `1 5`, `1 3`
   - Expected output: `0` (no changes needed for the entire string), `1` (change `a[1]` to `d`)

2. **Test Case 2**:
   - `n = 4`, `q = 2`
   - `a = "zzde"`, `b = "azbe"`
   - Queries: `1 3`, `1 4`
   - Expected output: `2` (change `a[1]` to `a` and `a[2]` to `z`), `2` (change `a[1]` to `a` and `a[2]` to `z`)

3. **Test Case 3**:
   - `n = 6`, `q = 3`
   - `a = "uwuwuw"`, `b = "wuwuwu"`
   - Queries: `2 4`, `1 3`, `1 6`
   - Expected output: `1` (change `a[2]` to `w`), `1` (change `a[1]` to `w`), `0` (no changes needed for the entire string)

4. **Test Case 4**:
   - `n = 8`, `q = 4`
   - `a = "abcdeabc"`, `b = "bcdeabcd"`
   - Queries: `1 8`, `1 4`, `5 8`, `3 6`
   - Expected output: `4` (change `a[1]` to `b`, `a[2]` to `c`, `a[3]` to `d`, `a[4]` to `e`), `1` (change `a[1]` to `b`), `1` (change `a[5]` to `a`), `1` (change `a[3]` to `b`)

This test input should expose the bug in the given code by challenging its logic in various scenarios.

4
5 2
abcde
edcba
1 5
1 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
8 4
abcdeabc
bcdeabcd
1 8
1 4
5 8
3 6


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include <bits/stdc++.h>
using namespace std;

int main() {
    int t;
    cin >> t;

    while(t--){
        int n, q;
        cin >> n >> q;
        string a, b;
        cin >> a >> b;

        for(int i=0; i<q; i++){
            int l, r;
            cin >> l >> r;

            l = l - 1;
            r = r - 1;

            map<char, int> mA, mB;
            for(int i=l; i<=r; i++){
                mA[a[i]]++;
                mB[b[i]]++;
            }

            int count = 0, set = 0;
            for(auto i: mB){
                if(mA.find(i.first) == mA.end()){
                    count = count + i.second;
                    set = set + i.second;
                }else{
                    int num = abs(i.second - mA[i.first]);
                    if(set >= num){
                        set = set - num;
                    }else{
                        count = count + num - set;
                        set = num - set;
                    }
                }
            }
            cout << count << endl;
        }
    }

    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include <cstring>
#include <iostream>

using namespace std;

const int maxn = 2e5 + 10;

int t;
int n, q;
int s[maxn];
char a[maxn], b[maxn];
int pa[30][maxn], pb[30][maxn];

int main()
{
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    std::cout.tie(0);

    cin >> t;
    while (t--) {
        cin >> n >> q;
        cin >> (a + 1) >> (b + 1);
        memset(pa[0], 0, sizeof pa[0]);
        memset(pb[0], 0, sizeof pb[0]);
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < 26; j++)
                pa[i][j] = pa[i - 1][j], pb[i][j] = pb[i - 1][j];
            pa[i][a[i] - 'a']++, pb[i][b[i] - 'a']++;
        }
        while (q--) {
            int l, r;
            cin >> l >> r;
            if (l > r)
                swap(l, r);
            int ans = 0;
            for (int i = 0; i < 26; i++) {
                ans += (pa[r][i] - pa[l - 1][i] != pb[r][i] - pb[l - 1][i]);
            }
            cout << ans / 2 << "\n";
        }
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
from collections import Counter
def fun(l,ll):
    d=Counter(l)
    dd=Counter(ll)
    c=0
    for i in d:
        if i not in dd:
            c+=d[i]
        else:
            if abs(d[i]-dd[i])>c:
                c=abs(d[i]-dd[i])
    return c
for _ in range(int(input())):
    n,k=map(int,input().split(" "))
    a=input()
    b=input()
    for __ in range(k):
        low,high=map(int,input().split(" "))
        l=list(a[low-1:high])
        ll=list(b[low-1:high])
        print(fun(l,ll))

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
def diffs(f, b, s, e):
    r = 0
    for i in "abcdefghijklmnopqrstuvwxyz":
        r += abs(f[i][e]+b[i][-s] - f[i][-1])
    return r//2

for _ in range(int(input())):
    n, k = map(int, input().split())
    a = input()
    b = input()
    s = "abcdefghijklmnopqrstuvwxyz"
    front = {}
    back = {}
    for i in s:
        front[i] = [0]
        back[i] = [0]
    for i in range(n):
        if a[i] != b[i]:
            front[a[i]].append(front[a[i]][-1]+1)
            front[b[i]].append(front[b[i]][-1]-1)
        else:
            front[a[i]].append(front[a[i]][-1])
        if a[-1-i] != b[-1-i]:
            back[b[-1-i]].append(back[b[-1-i]][-1]-1)
            back[a[-1-i]].append(back[a[-1-i]][-1]+1)
        else:
            back[a[-1-i]].append(back[a[-1-i]][-1])
        for w in s:
            if w != a[i] and w != b[i]:
                front[w].append(front[w][-1])
                back[w].append(back[w][-1])
    for i in range(k):
        l, r = map(int, input().split())
        print(diffs(front, back, l, r))

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
```

3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
def solve():
    import sys
    input = sys.stdin.read
    data = input().split()

    t = int(data[0])
    index = 1

    for _ in range(t):
        n, q = int(data[index]), int(data[index+1])
        index += 2

        a = data[index]
        b = data[index+1]
        index += 2

        # Precompute differences
        diff = [[0] * (n + 1) for _ in range(26)]
        for i in range(n):
            for c in range(26):
                diff[c][i + 1] = diff[c][i]
            diff[ord(a[i]) - ord('a')][i + 1] += 1
            diff[ord(b[i]) - ord('a')][i + 1] -= 1

        # Process queries
        results = []
        for _ in range(q):
            l, r = int(data[index]), int(data[index+1])
            l, r = l - 1, r  # adjust to 0-index
            index += 2

            changes = sum(1 for c in range(26) if diff[c][r] != diff[c][l])
            # Since we can fix two mismatches with one operation, we divide by 2
            results.append((changes + 1) // 2)  # +1 before division to round up

        for res in results:
            print(res)

# This script reads all input at once which might not be optimal for very large inputs
# but works for the constraints given in the problem.
solve()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
2 4
3 5
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import java.util.*;

public class Main{
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int t= sc.nextInt();
        ArrayList<Integer> ans=new ArrayList<>();
        for (int i = 0; i < t; i++) {
            int n= sc.nextInt();
            int q= sc.nextInt();
            String a=sc.next();
            String b= sc.next();
            int[][] query=new int[q][2];
            for (int j = 0; j < q; j++) {
                for (int k = 0; k < 2; k++) {
                    query[j][k]= sc.nextInt();
                }
            }
            for (int j = 0; j < q; j++) {
                HashMap<Character,Integer> map=new HashMap<>();
                HashMap<Character,Integer> map2=new HashMap<>();
                for (int k = query[j][0]-1; k <=query[j][1]-1 ; k++) {
                    char c=a.charAt(k);
                    map.put(c, map.getOrDefault(c,0)+1);
                    char ch=b.charAt(k);
                    map2.put(ch, map2.getOrDefault(ch,0)+1);
                }
                int sum=0;
                List<Integer> m1=new ArrayList<>();
                List<Integer> m2=new ArrayList<>();
                for (Character l:map.keySet()) {
                    Integer x=map.get(l);
                    Integer y=map2.get(l);
                    if(y==null){
                        sum+=x;
                    }
                    else if (x!=y) {
                        m1.add(x);
                        m2.add(y);
                    }
                }
                int hi=0;
                int l=0;
                for (int k = 0; k < m1.size(); k++) {
                    int x=m1.get(k);
                    int y=m2.get(k);
                    if(x>y)
                        hi+=x-y;
                    else
                        l+=y-x;
                }
                sum+=hi-l+Math.min(hi,l);
                ans.add(sum);
            }
        }
        for (Integer u:ans) {
            System.out.println(u);
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt(), ans, q, l, r, n;
        String a, b;
        for (int i = 0; i < t; i++) {
            n = sc.nextInt();
            int[] cnt = new int[26];
            int[] c = new int[n + 1];
            q = sc.nextInt();
            a = sc.next();
            b = sc.next();
            for (int x = 1; x <= n; x++) {
                cnt[a.charAt(x - 1) - 'a']++;
                cnt[b.charAt(x - 1) - 'a']--;
                for (int y = 0; y < 26; y++)
                    c[x] += Math.abs(cnt[y]);
            }
            for (int j = 0; j < q; j++) {
                l = sc.nextInt();
                r = sc.nextInt();
                System.out.println(Math.abs(c[r] - c[l - 1]) / 2);
            }
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To expose the bug in the given code, we need to create a test case that maximizes the failure probability. The bug in the code is related to the way it calculates the difference in character counts between the two strings. Specifically, the code incorrectly accumulates the differences and then tries to divide by 2 to get the number of operations. This can lead to incorrect results in certain scenarios.

### Step-by-Step Analysis:

1. **Understanding the Bug**:
   - The code uses a cumulative count array `c` to store the sum of absolute differences in character counts up to each position.
   - When calculating the answer for a query, it subtracts the cumulative count at `l-1` from the cumulative count at `r` and then divides by 2.
   - This approach can fail if the characters in the range `[l, r]` are not uniformly distributed or if the differences in character counts are not symmetric.

2. **Edge Cases**:
   - **Case 1**: All characters in `a` and `b` are the same in the range `[l, r]`.
   - **Case 2**: All characters in `a` and `b` are different in the range `[l, r]`.
   - **Case 3**: The characters in `a` and `b` are partially the same and partially different in the range `[l, r]`.
   - **Case 4**: The range `[l, r]` is the entire string.

3. **Creating a Test Case**:
   - We need a test case where the cumulative differences are not symmetric, and the division by 2 results in an incorrect number of operations.
   - A good candidate is a case where the characters in `a` and `b` are mostly the same but have a few differences that are not evenly distributed.

### Test Case:

```plaintext
1
5 3
abcde
abcdx
1 5
1 4
3 3
```

### Explanation:
- **Test Case**:
  - `n = 5`, `q = 3`
  - `a = "abcde"`, `b = "abcdx"`
  - Queries: `1 5`, `1 4`, `3 3`

- **Expected Output**:
  - For the first query (1 5):
    - `a[1..5] = "abcde"`, `b[1..5] = "abcdx"`
    - To make `a[1..5]` equal to `b[1..5]`, we need to change `e` to `x`.
    - Output: `1`
  - For the second query (1 4):
    - `a[1..4] = "abcd"`, `b[1..4] = "abcd"`
    - No changes are needed.
    - Output: `0`
  - For the third query (3 3):
    - `a[3..3] = "c"`, `b[3..3] = "c"`
    - No changes are needed.
    - Output: `0`

### Final Test Input:
```plaintext
1
5 3
abcde
abcdx
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
#define mod 1000000007
#define pi 3.141592653589793238462643383279502884197
#define all(ar) ar.begin(), ar.end()
#define rall(ar) ar.rbegin(), ar.rend()
typedef long long ll;
#define S second
#define F first
#define MAX(x) *max_element(all(x));
#define MIN(x) *min_element(all(x));
#define clz(x) __builtin_clz(x) // count leading zeros of 32 bits.
                                // like 4=00000000....100(leading 29 ta)
#define ctz(x) __builtin_ctz(x) // count trailing zeros
#define pb push_back
#define SUM(a) accumulate(all(a), 0LL)
void solve()
{
    string a, b;
    ll n, q;
    cin >> n >> q;
    cin >> a >> b;

    while (q--)
    {
        ll x, y;
        cin >> x >> y;
        map<char, ll> aa, bb;
        for (ll i = x - 1; i < y; i++)
        {
            aa[a[i]]++;
            bb[b[i]]++;
        }
        ll co = 0;
        for (char c = 'a'; c <= 'z'; c++)
        {
            if (aa[c] > 0 and bb[c] > 0)
            {
                co+=min(aa[c],bb[c]);
            }

        }
        ll qq = (y - x + 1);
        ll ans = qq - co;
        cout << ans << "\n";
        aa.clear();
        bb.clear();
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t;
    cin >> t;
    while (t--)
    {
        solve();
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given code, let's consider the following aspects:

1. **Edge Cases**:
   - Empty or nearly empty ranges (e.g., `l = r`).
   - Ranges that cover the entire string.
   - Ranges that cover parts of the string with very different characters.

2. **Character Distribution**:
   - Ensure that the strings `a` and `b` have different character distributions within the query ranges to maximize the number of operations required.

3. **Query Patterns**:
   - Queries that overlap or are nested within each other.
   - Queries that are at the boundaries of the string.

Let's construct a test input that includes these aspects:

```plaintext
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
```

This test input includes:
- A test case with a full range query and a partial range query.
- A test case with a short string and overlapping queries.
- A test case with a longer string and nested queries.

This should help in exposing any issues in the code, particularly in handling different character distributions and query ranges.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include <bits/stdc++.h>
#define let auto
using namespace std;
using ll = long long;

int f(string& s1, string& s2, int l, int r) {
  int ret = 0;
  multiset<char> s;
  for (int i = l; i <= r; i++) {
    s.insert(s1[i]);
  }
  for (int i = l; i <= r; i++) {
    char c = s2[i];
    let found = s.find(c);
    if (found != s.end()) {
      s.extract(found);
    } else {
      ret++;
    }
  }
  return ret;
}

int main() {
  iostream::sync_with_stdio(false); cin.tie();
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, q;
    string s1, s2;
    cin >> n >> q >> s1 >> s2;
    for (int qi = 0; qi < q; qi++) {
      int l, r;
      cin >> l >> r;
      l--; r--;
      cout << f(s1, s2, l, r) << "\n";
    }
  }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided code, we need to focus on edge cases and scenarios where the code might fail. The main issue in the buggy code is the handling of the range and the comparison of characters. Let's consider a few scenarios:

1. **Empty Range**: Ensure the code handles empty ranges correctly.
2. **Single Character Range**: Test with a single character to see if the code can handle it correctly.
3. **Range with All Characters Matching**: Ensure the code returns 0 when all characters in the range match.
4. **Range with All Characters Mismatching**: Ensure the code returns the correct number of operations when all characters in the range mismatch.
5. **Mixed Range**: Test with a range where some characters match and some do not.

Given these scenarios, let's create a small-scale test input:

```plaintext
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
```

This input includes:
1. A test case with a range covering the entire string.
2. A test case with a range covering most of the string.
3. A test case with a single character range.
4. A test case with a small range.
5. A test case with a mixed range.

This input should help expose any issues in the buggy code, particularly in how it handles ranges and character comparisons.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import sys

input = sys.stdin.readline

t = int(input())

for _ in range(t):
    n, q = tuple(map(int, input().split()))

    a = input()
    b = input()

    aprefix = [[0]*26 for _ in range(n+1)]
    bprefix = [[0]*26 for _ in range(n+1)]

    for i in range(1,n+1):
        for j in range(26):
            aprefix[i][j] = aprefix[i-1][j]
            bprefix[i][j] = bprefix[i-1][j]

        aprefix[i][ord(a[i-1])-ord('a')] += 1
        bprefix[i][ord(b[i-1])-ord('a')] += 1

    for _ in range(q):
        l, r = tuple(map(int, input().split()))

        res = 0
        for i in range(26):
            ansa = abs(aprefix[r][i]-aprefix[l-1][i])
            ansb = abs(bprefix[r][i]-bprefix[l-1][i])
            res += (abs(ansb-ansa))
        print(res//2)

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import sys

def readline() -> str:
    return sys.stdin.readline().strip()

def inputArray() -> list:
    return list(map(int, sys.stdin.readline().strip().split()))

def tc(solve):
    for _ in range(int(input())):
        solve()
    return
import math
import bisect
@tc
def solve():
    n,q=inputArray()
    a=input()
    b=input()

    for _ in range(q):
        l,r=inputArray()
        l=l-1
        r=r-1
        count_a = [0] * 26
        count_b = [0] * 26

        # Count characters in a[l..r] and b[l..r]
        for i in range(l, r + 1):
            count_a[ord(a[i]) - ord('a')] += 1
            count_b[ord(b[i]) - ord('a')] += 1

        # Calculate the number of operations
        operations = 0
        for i in range(26):
            operations += abs(count_a[i] - count_b[i])

        # Each operation can fix one difference in both strings
        print(operations // 2)

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given code, let's consider a few key points:

1. **Edge Cases:**
   - Single character strings.
   - Strings with all characters the same.
   - Strings where the characters are already sorted.
   - Strings where the characters are reverse sorted.

2. **Query Scenarios:**
   - Queries covering the entire string.
   - Queries covering a single character.
   - Queries covering the middle of the string.
   - Queries covering the start and end of the string.

3. **Character Distribution:**
   - Strings with a high frequency of certain characters.
   - Strings with a uniform distribution of characters.

Given these considerations, let's create a test input that includes a mix of these scenarios:

```plaintext
4
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
8 3
aabbccdd
ddccbbaa
1 8
3 6
2 7
```

### Explanation:
1. **First Test Case:**
   - Strings: "abcde" and "edcba"
   - Queries: (1, 5), (1, 4), (3, 3)
   - This case tests the full range, a range with one character difference, and a single character range.

2. **Second Test Case:**
   - Strings: "zzde" and "azbe"
   - Queries: (1, 3), (1, 4)
   - This case tests a range where the characters are already sorted and a range with a mix of characters.

3. **Third Test Case:**
   - Strings: "uwuwuw" and "wuwuwu"
   - Queries: (2, 4), (1, 3), (1, 6)
   - This case tests a range with repeating characters and a full range.

4. **Fourth Test Case:**
   - Strings: "aabbccdd" and "ddccbbaa"
   - Queries: (1, 8), (3, 6), (2, 7)
   - This case tests a full range with a uniform distribution of characters and sub-ranges with different distributions.

This test input should help expose any issues in the buggy code, especially in handling different character distributions and query ranges.

4
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
8 3
aabbccdd
ddccbbaa
1 8
3 6
2 7


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner s= new Scanner(System.in);
        int t = s.nextInt();

        while (t-- > 0) {

            int n = s.nextInt();
            int q = s.nextInt();
            String a = s.next();
            String b = s.next();
            while (q-- > 0) {
                int l = s.nextInt() - 1;
                int r = s.nextInt() - 1;

                int[] freqA = new int[26];
                int[] freqB = new int[26];

                for (int i = l; i <= r; i++) {
                    freqA[a.charAt(i) - 'a']++;
                    freqB[b.charAt(i) - 'a']++;
                }

                int changes = 0;
                for (int i = 0; i < 26; i++) {
                    changes += Math.abs(freqA[i] - freqB[i]);
                }

                System.out.println(changes / 2);
            }
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
6 3
abcabc
bcacba
1 3
2 4
1 6
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
import java.util.*;
import java.io.*;

public class Sort {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int t = Integer.parseInt(br.readLine());

        while (t-- > 0) {
            StringTokenizer st = new StringTokenizer(br.readLine());
            int n = Integer.parseInt(st.nextToken());
            int q = Integer.parseInt(st.nextToken());
            String a = br.readLine();
            String b = br.readLine();

            while (q-- > 0) {
                st = new StringTokenizer(br.readLine());
                int l = Integer.parseInt(st.nextToken()) - 1;
                int r = Integer.parseInt(st.nextToken()) - 1;

                int[] freqA = new int[26];
                int[] freqB = new int[26];

                for (int i = l; i <= r; ++i) {
                    freqA[a.charAt(i) - 'a']++;
                    freqB[b.charAt(i) - 'a']++;
                }

                int changes = 0;
                for (int i = 0; i < 26; ++i) {
                    changes += Math.abs(freqA[i] - freqB[i]);
                }
                out.println(changes / 2);
            }
        }
        out.flush();
        out.close();
        br.close();
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on scenarios where the frequency count approach might fail. The key issue in the buggy code is that it calculates the total number of changes required to make the frequency counts of the characters in the substring match, but it doesn't account for the fact that some characters might need to be moved multiple times to achieve the sorted order.

Here are the steps to create a challenging test input:

1. **Edge Cases:**
   - Test with a single character.
   - Test with identical strings.
   - Test with completely different strings.
   - Test with a string where the characters are already sorted.
   - Test with a string where the characters are in reverse sorted order.

2. **Scenario that Maximizes Failure:**
   - Create a string where the characters in the range [l, r] have a significant overlap in frequency but require a large number of operations to be sorted.

3. **Small-Scale Test Input:**
   - Use a small number of test cases.
   - Use a small length for the strings.
   - Use a small number of queries.

Given these considerations, here is a small-scale test input that is complete and valid:

```plaintext
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
```

This test input includes:
- A test case with strings "abcde" and "edcba" with queries that cover the entire string and smaller ranges.
- A test case with strings "zzde" and "azbe" with queries that cover different ranges.
- A test case with strings "uwuwuw" and "wuwuwu" with queries that cover different ranges.

This should help expose any issues in the frequency count approach used in the buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Sort
time_limit_ms: 5000
memory_limit_mb: 256
Description: You are given two strings $a$ and $b$ of length $n$. Then, you are (forced against your will) to answer $q$ queries.

For each query, you are given a range bounded by $l$ and $r$. In one operation, you can choose an integer $i$ ($l \leq i \leq r$) and set $a_i = x$ where $x$ is any character you desire. Output the minimum number of operations you must perform such that $\texttt{sorted(a[l..r])} = \texttt{sorted(b[l..r])}$. The operations you perform on one query does not affect other queries.

For an arbitrary string $c$, $\texttt{sorted(c[l..r])}$ denotes the substring consisting of characters $c_l, c_{l+1}, ... , c_r$ sorted in lexicographical order.

Input: The first line contains $t$ ($1 \leq t \leq 1000$) – the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) – the length of both strings and the number of queries.

The following line contains $a$ of length $n$. It is guaranteed $a$ only contains lowercase latin letters.

The following line contains $b$ of length $n$. It is guaranteed $b$ only contains lowercase latin letters.

The following $q$ lines contain two integers $l$ and $r$ ($1 \leq l \leq r \leq n$) – the range of the query.

It is guaranteed the sum of $n$ and $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output an integer, the minimum number of operations you need to perform in a new line.

Examples:
input:
3
5 3
abcde
edcba
1 5
1 4
3 3
4 2
zzde
azbe
1 3
1 4
6 3
uwuwuw
wuwuwu
2 4
1 3
1 6
output:
0
1
0
2
2
1
1
0

Note: For the first query, $\texttt{sorted(a[1..5])} =$ abcde and $\texttt{sorted(b[1..5])} =$ abcde, so no operations are necessary.

For the second query, you need to set $a_1 = $ e. Then, $\texttt{sorted(a[1..4])} = \texttt{sorted(b[1..4])} = $ bcde.

Buggy Code:
#include<algorithm>
#include<iostream>
#include<vector>
#include<cmath>
#include<map>
using namespace std;
typedef long long ll;
ll t, n, q, l, r;
string a, b;
int main()
{
	ios::sync_with_stdio(false), cin.tie(0);
	cin >> t;
	while (t--) {
		cin >> n >> q;
		cin >> a >> b;
		vector<map<char,int>>va(n + 1),vb(n + 1);
		for (int i = 0; i < n; i++) {
			va[i + 1] = va[i], vb[i + 1] = vb[i];
			va[i + 1][a[i]]++;
			vb[i + 1][b[i]]++;
		}
		while (q--) {
			cin >> l >> r;
			int sum = 0;
			for (char i = 'a'; i <= 'z'; i++) {
				int x = va[r][i] - va[l - 1][i], y = vb[r][i] - vb[l - 1][i];
				sum += abs(x - y);
			}
			cout << sum / 2 << endl;
		}
	}
	return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
5 3
abcde
edcba
1 5
1 4
3 3
```