Shohag has an integer sequence a_1, a_2, …, a_n. He can perform the following operation any number of times (possibly, zero):

  * Select any positive integer k (it can be different in different operations). 
  * Choose any position in the sequence (possibly the beginning or end of the sequence, or in between any two elements) and insert k into the sequence at this position. 
  * This way, the sequence a changes, and the next operation is performed on this changed sequence. 



For example, if a=[3,3,4] and he selects k = 2, then after the operation he can obtain one of the sequences [\underline{2},3,3,4], [3,\underline{2},3,4], [3,3,\underline{2},4], or [3,3,4,\underline{2}].

Shohag wants this sequence to satisfy the following condition: for each 1 ≤ i ≤ |a|, a_i ≤ i. Here, |a| denotes the size of a.

Help him to find the minimum number of operations that he has to perform to achieve this goal. We can show that under the constraints of the problem it's always possible to achieve this goal in a finite number of operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 200) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the initial length of the sequence.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the sequence.

Output

For each test case, print a single integer — the minimum number of operations needed to perform to achieve the goal mentioned in the statement.

Example

Input


4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969


Output


1
3
0
696966

Note

In the first test case, we have to perform at least one operation, as a_2=3>2. We can perform the operation [1, 3, 4] → [1, \underline{2}, 3, 4] (the newly inserted element is underlined), now the condition is satisfied.

In the second test case, Shohag can perform the following operations:

[1, 2, 5, 7, 4] → [1, 2, \underline{3}, 5, 7, 4] → [1, 2, 3, \underline{4}, 5, 7, 4] → [1, 2, 3, 4, 5, \underline{3}, 7, 4].

In the third test case, the sequence already satisfies the condition.
1
39
481199252 336470888 634074578 642802746 740396295 773386884 579721198 396628655 503722503 971207868 202647942 2087506 268792718 46761498 443917727 16843338 125908043 691952768 717268783 787375312 150414369 693319712 519096230 45277106 856168102 762263554 674936674 407246545 274667941 279198849 527268921 155191459 421436316 536134606 286802932 140515506 646837311 233465964 451394766

971207858

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.stream.Collectors;

public class Main {
    static int mod = (int) (1e9) + 7;

    /* ======================DSU===================== */
    static class dsu {
        static int parent[], n;// min[],value[];
        static long size[];

        dsu(int n) {
            parent = new int[n + 1];
            size = new long[n + 1];
            // min=new int[n+1];
            // value=new int[n+1];
            Main.dsu.n = n;
            makeSet();
        }

        static void makeSet() {
            for (int i = 1; i <= n; i++) {
                parent[i] = i;
                size[i] = 1;
                // min[i]=i;
            }
        }

        static int find(int a) {
            if (parent[a] == a)
                return a;
            else {
                return parent[a] = find(parent[a]);// Path Compression
            }
        }

        static void union(int a, int b) {
            int setA = find(a);
            int setB = find(b);
            if (setA == setB)
                return;
            if (size[setA] >= size[setB]) {
                parent[setB] = setA;
                size[setA] += size[setB];
            } else {
                parent[setA] = setB;
                size[setB] += size[setA];
            }
        }
    }

    /* ======================================================== */
    static class Pair<X extends Number, Y extends Number> implements Comparator<Pair> {
        X x;
        Y y;

        // Constructor
        public Pair(X x, Y y) {
            this.x = x;
            this.y = y;
        }

        public Pair() {

        }

        @Override
        public int compare(Main.Pair o1, Main.Pair o2) {
            return ((int) (o1.y.intValue() - o2.y.intValue()));// Ascending Order based on 'y'
        }
    }

    /* ===============================Tries================================= */
    static class TrieNode {
        private HashMap<Character, TrieNode> children = new HashMap<>();
        public int size;
        boolean endOfWord;

        public void putChildIfAbsent(char ch) {
            children.putIfAbsent(ch, new TrieNode());
        }

        public TrieNode getChild(char ch) {
            return children.get(ch);
        }
    }

    static private TrieNode root;

    public static void insert(String str) {
        TrieNode curr = root;
        for (char ch : str.toCharArray()) {
            curr.putChildIfAbsent(ch);
            curr = curr.getChild(ch);
            curr.size++;
        }
        // mark the current nodes endOfWord as true
        curr.endOfWord = true;
    }

    public static int search(String word) {
        TrieNode curr = root;

        for (char ch : word.toCharArray()) {
            curr = curr.getChild(ch);
            if (curr == null) {
                return 0;
            }
        }
        // size contains words starting with prefix- word
        return curr.size;
    }

    public boolean delete(TrieNode current, String word, int index) {
        if (index == word.length()) {
            // when end of word is reached only delete if currrent.endOfWord is true.
            if (!current.endOfWord) {
                return false;
            }
            current.endOfWord = false;
            // if current has no other mapping then return true
            return current.children.size() == 0;
        }
        char ch = word.charAt(index);
        TrieNode node = current.children.get(ch);
        if (node == null) {
            return false;
        }
        boolean shouldDeleteCurrentNode = delete(node, word, index + 1);

        // if true is returned then delete the mapping of character and trienode
        // reference from map.
        if (shouldDeleteCurrentNode) {
            current.children.remove(ch);
            // return true if no mappings are left in the map.
            return current.children.size() == 0;
        }
        return false;
    }

    /* ================================================================= */

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (long i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static Pair<Integer, Integer> lowerBound(long[] a, long x) { // x is the target, returns lowerBound. If not found
                                                                 // return -1
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] == x) {
                return new Pair<>(m, 1);
            }
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return new Pair<>(r, 0);
    }

    static Pair<Integer, Integer> upperBound(long[] a, long x) {// x is the target, returns upperBound. If not found
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] == x) {
                return new Pair<>(m, 1);
            }
            if (a[m] <= x)
                l = m;
            else
                r = m;
        }
        return new Pair<>(l + 1, 0);
    }

    static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x);
            y >>= 1;
            x = (x * x);
        }
        return res;
    }

    public double binPow(double x, int n) {// binary exponentiation with negative power as well
        if (n == 0)
            return 1.0;
        double binPow = binPow(x, n / 2);
        if (n % 2 == 0) {
            return binPow * binPow;
        } else {
            return n > 0 ? (binPow * binPow * x) : (binPow * binPow / x);
        }
    }

    static long ceil(long x, long y) {
        return (x % y == 0 ? x / y : (x / y + 1));
    }

    /*
     * ===========Modular Operations==================
     */
    static long modPower(long x, long y, long p) {
        long res = 1;
        x = x % p;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }
        return res;
    }

    static long modInverse(long n, long p) {
        return modPower(n, p - 2, p);
    }

    static long modAdd(long a, long b) {
        return ((a + b + mod) % mod);
    }

    static long modMul(long a, long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    static long[] fac = new long[200000 + 5];
    static long[] invFac = new long[200000 + 5];

    static long nCrModPFermat(int n, int r) {
        if (r == 0)
            return 1;
        // return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod)
        // % mod) % mod;
        return (fac[n] * invFac[r] % mod * invFac[n - r] % mod) % mod;
    }

    /*
     * ===============================================
     */

    static void ruffleSort(long[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            long temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            int temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static String binString32(int n) {
        StringBuilder str = new StringBuilder("");
        String bin = Integer.toBinaryString(n);
        if (bin.length() != 32) {
            for (int k = 0; k < 32 - bin.length(); k++) {
                str.append("0");
            }
            str.append(bin);
        }
        return str.toString();
    }

    static class sparseTable {
        public static int st[][];
        public static int log = 4;

        static int func(int a, int b) {// make func as per question(here min range query)
            return (int) gcd(a, b);
        }

        void makeTable(int n, int a[]) {

            st = new int[n][log];
            for (int i = 0; i < n; i++) {
                st[i][0] = a[i];
            }
            for (int j = 1; j < log; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    st[i][j] = func(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
                }
            }
        }

        static int query(int l, int r) {
            int length = r - l + 1;
            int k = 0;
            while ((1 << (k + 1)) <= length) {
                k++;
            }
            return func(st[l][k], st[r - (1 << k) + 1][k]);
        }

        static void printTable(int n) {
            for (int j = 0; j < log; j++) {
                for (int i = 0; i < n; i++) {
                    System.out.print(st[i][j] + " ");
                }
                System.out.println();
            }
        }
    }

    /*
     * ====================================Main=================================
     */

    // static int st[], a[];

    // static void buildTree(int treeIndex, int lo, int hi) {
    // if (hi == lo) {
    // st[treeIndex] = a[lo];
    // return;
    // }
    // int mid = (lo + hi) / 2;
    // buildTree(treeIndex * 2 + 1, lo, mid);
    // buildTree(treeIndex * 2 + 2, mid + 1, hi);
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
    // if (hi == lo) {
    // st[treeIndex] = val;
    // a[arrIndex] = val;
    // return;
    // }
    // int mid = (hi + lo) / 2;
    // if (mid < arrIndex) {
    // update(treeIndex * 2 + 2, mid + 1, hi, arrIndex, val);
    // } else {
    // update(treeIndex * 2 + 1, lo, mid, arrIndex, val);
    // }
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static int query(int treeIndex, int lo, int hi, int l, int r) {
    // if (l <= lo && r >= hi) {
    // return st[treeIndex];
    // }
    // if (l > hi || r < lo) {
    // return 0;
    // }
    // int mid = (hi + lo) / 2;
    // return query(treeIndex * 2 + 1, lo, mid, l, Math.min(mid, r));
    // }

    // static int merge(int a, int b) {
    // return a + b;
    // }

    public static long findKthPositive(long[] A, long k) {
        int l = 0, r = A.length, m;
        while (l < r) {
            m = (l + r) / 2;
            if (A[m] - 1 - m < k)
                l = m + 1;
            else
                r = m;
        }
        return l + k;
    }

    static int[] z_function(char ar[]) {
        int[] z = new int[ar.length];
        z[0] = ar.length;
        int l = 0;
        int r = 0;
        for (int i = 1; i < ar.length; i++) {
            if (r < i) {
                l = i;
                r = i;
                while (r < ar.length && ar[r - l] == ar[r])
                    r++;
                z[i] = r - l;
                r--;
            } else {
                int k = i - l;
                if (z[k] < r - i + 1) {
                    z[i] = z[k];
                } else {
                    l = i;
                    while (r < ar.length && ar[r - l] == ar[r])
                        r++;
                    z[i] = r - l;
                    r--;
                }
            }
        }
        return z;
    }

    static void mergeSort(int a[]) {
        int n = a.length;
        if (n >= 2) {
            int mid = n / 2;
            int left[] = new int[mid];
            int right[] = new int[n - mid];
            for (int i = 0; i < mid; i++) {
                left[i] = a[i];
            }
            for (int i = mid; i < n; i++) {
                right[i - mid] = a[i];
            }
            mergeSort(left);
            mergeSort(right);
            mergeSortedArray(left, right, a);
        }
    }

    static void mergeSortedArray(int left[], int right[], int a[]) {
        int i = 0, j = 0, k = 0, n = left.length, m = right.length;
        while (i != n && j != m) {
            if (left[i] < right[j]) {
                a[k++] = left[i++];
            } else {
                a[k++] = right[j++];
            }
        }
        while (i != n) {
            a[k++] = left[i++];
        }
        while (j != m) {
            a[k++] = right[j++];
        }
    }

    // BINARY SEARCH
    // count of set bits in a particular position
    // suffix max array/ suffix sum array/ prefix
    static 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 {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] intArr(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] longArr(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

    static FastReader f = new FastReader();
    static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String args[]) throws Exception {
        int t = 1;
        t = f.nextInt();
        int tc = 1;
        // fac[0] = 1;
        // for (int i = 1; i <= 200000; i++) {
        // fac[i] = fac[i - 1] * i % mod;
        // invFac[i] = modInverse(fac[i], mod);
        // }
        while (t-- != 0) {
            int n = f.nextInt();
            int a[] = new int[n];
            a = f.intArr(n);
            int pos = 1, moves = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] > pos) {
                    moves += -pos + a[i];
                    pos += -pos + a[i];
                }
                pos++;

            }
            w.write(moves + "\n");
        }
        w.flush();
    }
}
/*

 */