Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode). 
    
    
      
    procedure bubbleSortGraph()  
        build a graph G with n vertices and 0 edges  
        repeat  
            swapped = false  
            for i = 1 to n - 1 inclusive do:  
                if a[i] > a[i + 1] then  
                    add an undirected edge in G between a[i] and a[i + 1]  
                    swap( a[i], a[i + 1] )  
                    swapped = true  
                end if  
            end for  
        until not swapped   
        /* repeat the algorithm as long as swapped value is true. */   
    end procedure  
    

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n).

Output

Output a single integer — the answer to the problem. 

Examples

Input

3
3 1 2


Output

2

Note

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
100
36 48 92 87 28 85 42 10 44 41 39 3 79 9 14 56 1 16 46 35 93 8 82 26 100 59 60 2 96 52 13 98 70 81 71 94 54 91 17 88 33 30 19 50 18 73 65 29 78 21 61 7 99 97 45 89 57 27 76 11 49 72 84 69 43 62 4 22 75 6 66 83 38 34 86 15 40 51 37 74 67 31 20 63 77 80 12 53 5 25 58 90 68 24 64 23 95 32 55 47
 5
4 2 1 3 5
 10
1 9 8 10 2 3 4 6 5 7
 50
12 24 42 43 36 3 40 29 7 34 10 13 28 9 35 23 25 21 19 4 20 18 11 38 41 48 6 46 33 17 31 37 2 30 32 44 45 5 47 49 16 15 50 27 26 14 39 22 1 8

16
 3
 6
 13

import java.io.*;
import java.util.*;

public class icpc
{
    public static void main(String[] args) throws IOException
    {
        Reader in = new Reader();
        //BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = in.nextInt();
        int[] A = new int[n];
        for (int i=0;i<n;i++)   A[i] = in.nextInt();
        System.out.println(LIS(A));
    }
    public static int LIS(int[] X)
    {
        int[] parent = new int[X.length];
        int[] increasingSub = new int[X.length + 1];
        int length = 0;

        for (int i=0;i<X.length;i++)
        {
            int low = 1;
            int high = length;
            while (low <= high)
            {
                int mid = (int)Math.ceil((low + high) / 2);

                if (X[increasingSub[mid]] < X[i])
                {
                    low = mid + 1;
                }
                else
                    high = mid - 1;
            }

            int pos = low;
            parent[i] = increasingSub[pos - 1];
            increasingSub[pos] = i;
            if (pos > length)
                length = pos;
        }
        return length;
    }
}
class DSU
{
    int[] parent;
    int[] size;
    //Pass number of total nodes as parameter to the constructor
    DSU(int n)
    {
        this.parent = new int[n];
        this.size = new int[n];
        Arrays.fill(parent, -1);
    }

    public void makeSet(int v)
    {
        parent[v] = v;
        size[v] = 1;
    }

    public int findSet(int v)
    {
        if (v == parent[v]) return v;
        return parent[v] = findSet(parent[v]);
    }

    public void unionSets(int a, int b)
    {
        a = findSet(a);
        b = findSet(b);
        if (a != b)
        {
            if (size[a] < size[b])
            {
                int temp = a;
                a = b;
                b = temp;
            }
            parent[b] = a;
            size[a] += size[b];
        }
    }
}
class FastFourierTransform
{
    private void fft(double[] a, double[] b, boolean invert)
    {
        int count = a.length;
        for (int i = 1, j = 0; i < count; i++)
        {
            int bit = count >> 1;
            for (; j >= bit; bit >>= 1)
                j -= bit;
            j += bit;
            if (i < j)
            {
                double temp = a[i];
                a[i] = a[j];
                a[j] = temp;
                temp = b[i];
                b[i] = b[j];
                b[j] = temp;
            }
        }
        for (int len = 2; len <= count; len <<= 1)
        {
            int halfLen = len >> 1;
            double angle = 2 * Math.PI / len;
            if (invert)
                angle = -angle;
            double wLenA = Math.cos(angle);
            double wLenB = Math.sin(angle);
            for (int i = 0; i < count; i += len)
            {
                double wA = 1;
                double wB = 0;
                for (int j = 0; j < halfLen; j++)
                {
                    double uA = a[i + j];
                    double uB = b[i + j];
                    double vA = a[i + j + halfLen] * wA - b[i + j + halfLen] * wB;
                    double vB = a[i + j + halfLen] * wB + b[i + j + halfLen] * wA;
                    a[i + j] = uA + vA;
                    b[i + j] = uB + vB;
                    a[i + j + halfLen] = uA - vA;
                    b[i + j + halfLen] = uB - vB;
                    double nextWA = wA * wLenA - wB * wLenB;
                    wB = wA * wLenB + wB * wLenA;
                    wA = nextWA;
                }
            }
        }
        if (invert)
        {
            for (int i = 0; i < count; i++)
            {
                a[i] /= count;
                b[i] /= count;
            }
        }
    }

    public long[] multiply(long[] a, long[] b)
    {
        int resultSize = Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2;
        resultSize = Math.max(resultSize, 1);
        double[] aReal = new double[resultSize];
        double[] aImaginary = new double[resultSize];
        double[] bReal = new double[resultSize];
        double[] bImaginary = new double[resultSize];
        for (int i = 0; i < a.length; i++)
            aReal[i] = a[i];
        for (int i = 0; i < b.length; i++)
            bReal[i] = b[i];
        fft(aReal, aImaginary, false);
        fft(bReal, bImaginary, false);
        for (int i = 0; i < resultSize; i++)
        {
            double real = aReal[i] * bReal[i] - aImaginary[i] * bImaginary[i];
            aImaginary[i] = aImaginary[i] * bReal[i] + bImaginary[i] * aReal[i];
            aReal[i] = real;
        }
        fft(aReal, aImaginary, true);
        long[] result = new long[resultSize];
        for (int i = 0; i < resultSize; i++)
            result[i] = Math.round(aReal[i]);
        return result;
    }
}
class NumberTheory
{
    public boolean isPrime(long n)
    {
        if(n < 2)
            return false;
        for(long x = 2;x * x <= n;x++)
        {
            if(n % x == 0)
                return false;
        }
        return true;
    }
    public ArrayList<Long> primeFactorisation(long n)
    {
        ArrayList<Long> f = new ArrayList<>();
        for(long x=2;x * x <= n;x++)
        {
            while(n % x == 0)
            {
                f.add(x);
                n /= x;
            }
        }
        if(n > 1)
            f.add(n);
        return f;
    }
    public int[] sieveOfEratosthenes(int n)
    {
        //Returns an array with the smallest prime factor for each number and primes marked as 0
        int[] sieve = new int[n + 1];
        for(int x=2;x * x <= n;x++)
        {
            if(sieve[x] != 0)
                continue;
            for(int u=x*x;u<=n;u+=x)
            {
                if(sieve[u] == 0)
                {
                    sieve[u] = x;
                }
            }
        }
        return sieve;
    }
    public long gcd(long a, long b)
    {
        if(b == 0)
            return a;
        return gcd(b, a % b);
    }
    public long phi(long n)
    {
        double result = n;

        for(long p=2;p*p<=n;p++)
        {
            if(n % p == 0)
            {
                while (n % p == 0)
                    n /= p;
                result *= (1.0 - (1.0 / (double)p));
            }
        }
        if(n > 1)
            result *= (1.0 - (1.0 / (double)n));
        return (long)result;
    }
    public Name extendedEuclid(long a, long b)
    {
        if(b == 0)
            return new Name(a, 1, 0);
        Name n1 = extendedEuclid(b, a % b);
        Name n2 = new Name(n1.d, n1.y, n1.x - (long)Math.floor((double)a / b) * n1.y);
        return n2;
    }
    public long modularExponentiation(long a, long b, long n)
    {
        long d = 1L;
        String bString = Long.toBinaryString(b);
        for(int i=0;i<bString.length();i++)
        {
            d = (d * d) % n;
            if(bString.charAt(i) == '1')
                d = (d * a) % n;
        }
        return d;
    }
}
class Name
{
    long d;
    long x;
    long y;

    public Name(long d, long x, long y)
    {
        this.d = d;
        this.x = x;
        this.y = y;
    }
}
class SuffixArray
{
    int ALPHABET_SZ = 256, N;
    int[] T, lcp, sa, sa2, rank, tmp, c;

    public SuffixArray(String str)
    {
        this(toIntArray(str));
    }

    private static int[] toIntArray(String s)
    {
        int[] text = new int[s.length()];
        for (int i = 0; i < s.length(); i++) text[i] = s.charAt(i);
        return text;
    }

    public SuffixArray(int[] text)
    {
        T = text;
        N = text.length;
        sa = new int[N];
        sa2 = new int[N];
        rank = new int[N];
        c = new int[Math.max(ALPHABET_SZ, N)];
        construct();
        kasai();
    }

    private void construct()
    {
        int i, p, r;
        for (i = 0; i < N; ++i) c[rank[i] = T[i]]++;
        for (i = 1; i < ALPHABET_SZ; ++i) c[i] += c[i - 1];
        for (i = N - 1; i >= 0; --i) sa[--c[T[i]]] = i;
        for (p = 1; p < N; p <<= 1)
        {
            for (r = 0, i = N - p; i < N; ++i) sa2[r++] = i;
            for (i = 0; i < N; ++i) if (sa[i] >= p) sa2[r++] = sa[i] - p;
            Arrays.fill(c, 0, ALPHABET_SZ, 0);
            for (i = 0; i < N; ++i) c[rank[i]]++;
            for (i = 1; i < ALPHABET_SZ; ++i) c[i] += c[i - 1];
            for (i = N - 1; i >= 0; --i) sa[--c[rank[sa2[i]]]] = sa2[i];
            for (sa2[sa[0]] = r = 0, i = 1; i < N; ++i)
            {
                if (!(rank[sa[i - 1]] == rank[sa[i]]
                        && sa[i - 1] + p < N
                        && sa[i] + p < N
                        && rank[sa[i - 1] + p] == rank[sa[i] + p])) r++;
                sa2[sa[i]] = r;
            }
            tmp = rank;
            rank = sa2;
            sa2 = tmp;
            if (r == N - 1) break;
            ALPHABET_SZ = r + 1;
        }
    }

    private void kasai()
    {
        lcp = new int[N];
        int[] inv = new int[N];
        for (int i = 0; i < N; i++) inv[sa[i]] = i;
        for (int i = 0, len = 0; i < N; i++)
        {
            if (inv[i] > 0)
            {
                int k = sa[inv[i] - 1];
                while ((i + len < N) && (k + len < N) && T[i + len] == T[k + len]) len++;
                lcp[inv[i] - 1] = len;
                if (len > 0) len--;
            }
        }
    }
}
class ZAlgorithm
{
    public int[] calculateZ(char input[])
    {
        int Z[] = new int[input.length];
        int left = 0;
        int right = 0;
        for(int k = 1; k < input.length; k++) {
            if(k > right) {
                left = right = k;
                while(right < input.length && input[right] == input[right - left]) {
                    right++;
                }
                Z[k] = right - left;
                right--;
            } else {
                //we are operating inside box
                int k1 = k - left;
                //if value does not stretches till right bound then just copy it.
                if(Z[k1] < right - k + 1) {
                    Z[k] = Z[k1];
                } else { //otherwise try to see if there are more matches.
                    left = k;
                    while(right < input.length && input[right] == input[right - left]) {
                        right++;
                    }
                    Z[k] = right - left;
                    right--;
                }
            }
        }
        return Z;
    }
    public ArrayList<Integer> matchPattern(char text[], char pattern[])
    {
        char newString[] = new char[text.length + pattern.length + 1];
        int i = 0;
        for(char ch : pattern) {
            newString[i] = ch;
            i++;
        }
        newString[i] = '$';
        i++;
        for(char ch : text) {
            newString[i] = ch;
            i++;
        }
        ArrayList<Integer> result = new ArrayList<>();
        int Z[] = calculateZ(newString);

        for(i = 0; i < Z.length ; i++) {
            if(Z[i] == pattern.length) {
                result.add(i - pattern.length - 1);
            }
        }
        return result;
    }
}
class KMPAlgorithm
{
    public int[] computeTemporalArray(char[] pattern)
    {
        int[] lps = new int[pattern.length];

        int index = 0;
        for(int i=1;i<pattern.length;)
        {
            if(pattern[i] == pattern[index])
            {
                lps[i] = index + 1;
                index++;
                i++;
            }
            else
            {
                if(index != 0)
                {
                    index = lps[index - 1];
                }
                else
                {
                    lps[i] = 0;
                    i++;
                }
            }
        }
        return lps;
    }

    public ArrayList<Integer> KMPMatcher(char[] text, char[] pattern)
    {
        int[] lps = computeTemporalArray(pattern);

        int j = 0;
        int i = 0;
        int n = text.length;
        int m = pattern.length;
        ArrayList<Integer> indices = new ArrayList<>();
        while(i < n)
        {
            if(pattern[j] == text[i])
            {
                i++;
                j++;
            }
            if(j == m)
            {
                indices.add(i - j);
                j = lps[j - 1];
            }
            else if(i < n && pattern[j] != text[i])
            {
                if(j != 0)
                    j = lps[j - 1];
                else
                    i = i + 1;
            }
        }
        return indices;
    }
}
class Hashing
{
    public long[] computePowers(long p, int n, long m)
    {
        long[] powers = new long[n];
        powers[0] = 1;
        for(int i=1;i<n;i++)
        {
            powers[i] = (powers[i - 1] * p) % m;
        }
        return powers;
    }
    public long computeHash(String s)
    {
        long p = 31;
        long m = 1_000_000_009;
        long hashValue = 0L;
        long[] powers = computePowers(p, s.length(), m);
        for(int i=0;i<s.length();i++)
        {
            char ch = s.charAt(i);
            hashValue = (hashValue + (ch - 'a' + 1) * powers[i]) % m;
        }
        return hashValue;
    }
}
class BasicFunctions
{
    public long min(long[] A)
    {
        long min = Long.MAX_VALUE;
        for(int i=0;i<A.length;i++)
        {
            min = Math.min(min, A[i]);
        }
        return min;
    }
    public long max(long[] A)
    {
        long max = Long.MAX_VALUE;
        for(int i=0;i<A.length;i++)
        {
            max = Math.max(max, A[i]);
        }
        return max;
    }
}
class MergeSortInt
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r) {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int[n1];
        int R[] = new int[n2];

        /*Copy data to temp arrays*/
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r) {
        if (l < r) {
            // Find the middle point
            int m = (l + r) / 2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr, m + 1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

}
class MergeSortLong
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(long arr[], int l, int m, int r) {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        long L[] = new long[n1];
        long R[] = new long[n2];

        /*Copy data to temp arrays*/
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(long arr[], int l, int r) {
        if (l < r) {
            // Find the middle point
            int m = (l + r) / 2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr, m + 1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }
}
class Node
{

    int x;
    int y;

    public Node(int x, int y)
    {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object ob)
    {
        if(ob == null)
            return false;
        if(!(ob instanceof Node))
            return false;
        if(ob == this)
            return true;
        Node obj = (Node)ob;
        if(this.x == obj.x && this.y == obj.y)
            return true;
        return false;
    }

    @Override
    public int hashCode()
    {
        return (int)this.x;
    }
}
class Reader
{
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException
    {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException
    {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1)
        {
            if (c == '\n')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do
        {
            ret = ret * 10 + c - '0';
        }  while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException
    {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException
    {
        if (din == null)
            return;
        din.close();
    }
}
class FenwickTree
{
    public void update(long[] fenwickTree,long delta,int index)
    {
        index += 1;
        while(index < fenwickTree.length)
        {
            fenwickTree[index] += delta;
            index = index + (index & (-index));
        }
    }
    public long prefixSum(long[] fenwickTree,int index)
    {
        long sum = 0L;
        index += 1;
        while(index > 0)
        {
            sum += fenwickTree[index];
            index -= (index & (-index));
        }
        return sum;
    }
}
class SegmentTree
{
    public int nextPowerOfTwo(int num)
    {
        if(num == 0)
            return 1;
        if(num > 0 && (num & (num - 1)) == 0)
            return num;
        while((num &(num - 1)) > 0)
        {
            num = num & (num - 1);
        }
        return num << 1;
    }
    public int[] createSegmentTree(int[] input)
    {
        int np2 = nextPowerOfTwo(input.length);
        int[] segmentTree = new int[np2 * 2 - 1];

        for(int i=0;i<segmentTree.length;i++)
            segmentTree[i] = Integer.MIN_VALUE;

        constructSegmentTree(segmentTree,input,0,input.length-1,0);
        return segmentTree;

    }
    private void constructSegmentTree(int[] segmentTree,int[] input,int low,int high,int pos)
    {
        if(low == high)
        {
            segmentTree[pos] = input[low];
            return;
        }
        int mid = (low + high)/ 2;
        constructSegmentTree(segmentTree,input,low,mid,2*pos + 1);
        constructSegmentTree(segmentTree,input,mid+1,high,2*pos + 2);
        segmentTree[pos] = Math.max(segmentTree[2*pos + 1],segmentTree[2*pos + 2]);
    }
    public int rangeMinimumQuery(int []segmentTree,int qlow,int qhigh,int len)
    {
        return rangeMinimumQuery(segmentTree,0,len-1,qlow,qhigh,0);
    }
    private int rangeMinimumQuery(int segmentTree[],int low,int high,int qlow,int qhigh,int pos)
    {
        if(qlow <= low && qhigh >= high){
            return segmentTree[pos];
        }
        if(qlow > high || qhigh < low){
            return Integer.MIN_VALUE;
        }
        int mid = (low+high)/2;
        return Math.max(rangeMinimumQuery(segmentTree, low, mid, qlow, qhigh, 2 * pos + 1),
                rangeMinimumQuery(segmentTree, mid + 1, high, qlow, qhigh, 2 * pos + 2));
    }
}
class Trie
{

    private class TrieNode
    {
        Map<Character, TrieNode> children;
        boolean endOfWord;
        public TrieNode()
        {
            children = new HashMap<>();
            endOfWord = false;
        }
    }

    private final TrieNode root;
    public Trie()
    {
        root = new TrieNode();
    }

    public void insert(String word)
    {
        TrieNode current = root;
        for (int i = 0; i < word.length(); i++)
        {
            char ch = word.charAt(i);
            TrieNode node = current.children.get(ch);
            if (node == null)
            {
                node = new TrieNode();
                current.children.put(ch, node);
            }
            current = node;
        }
        current.endOfWord = true;
    }

    public boolean search(String word)
    {
        TrieNode current = root;
        for (int i = 0; i < word.length(); i++)
        {
            char ch = word.charAt(i);
            TrieNode node = current.children.get(ch);
            if (node == null)
            {
                return false;
            }
            current = node;
        }
        return current.endOfWord;
    }

    public void delete(String word)
    {
        delete(root, word, 0);
    }

    private boolean delete(TrieNode current, String word, int index)
    {
        if (index == word.length())
        {
            if (!current.endOfWord)
            {
                return false;
            }
            current.endOfWord = false;
            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 (shouldDeleteCurrentNode)
        {
            current.children.remove(ch);
            return current.children.size() == 0;
        }
        return false;
    }
}
class SegmentTreeLazy
{
    public int nextPowerOfTwo(int num)
    {
        if(num == 0)
            return 1;
        if(num > 0 && (num & (num - 1)) == 0)
            return num;
        while((num &(num - 1)) > 0)
        {
            num = num & (num - 1);
        }
        return num << 1;
    }

    public int[] createSegmentTree(int input[])
    {
        int nextPowOfTwo = nextPowerOfTwo(input.length);
        int segmentTree[] = new int[nextPowOfTwo*2 -1];

        for(int i=0; i < segmentTree.length; i++){
            segmentTree[i] = Integer.MAX_VALUE;
        }
        constructMinSegmentTree(segmentTree, input, 0, input.length - 1, 0);
        return segmentTree;
    }

    private void constructMinSegmentTree(int segmentTree[], int input[], int low, int high,int pos)
    {
        if(low == high)
        {
            segmentTree[pos] = input[low];
            return;
        }
        int mid = (low + high)/2;
        constructMinSegmentTree(segmentTree, input, low, mid, 2 * pos + 1);
        constructMinSegmentTree(segmentTree, input, mid + 1, high, 2 * pos + 2);
        segmentTree[pos] = Math.min(segmentTree[2*pos+1], segmentTree[2*pos+2]);
    }

    public void updateSegmentTreeRangeLazy(int input[], int segmentTree[], int lazy[], int startRange, int endRange, int delta)
    {
        updateSegmentTreeRangeLazy(segmentTree, lazy, startRange, endRange, delta, 0, input.length - 1, 0);
    }

    private void updateSegmentTreeRangeLazy(int segmentTree[], int lazy[], int startRange, int endRange, int delta, int low, int high, int pos)
    {
        if(low > high)
        {
            return;
        }
        if (lazy[pos] != 0)
        {
            segmentTree[pos] += lazy[pos];
            if (low != high)
            {
                lazy[2 * pos + 1] += lazy[pos];
                lazy[2 * pos + 2] += lazy[pos];
            }
            lazy[pos] = 0;
        }

        if(startRange > high || endRange < low)
        {
            return;
        }

        if(startRange <= low && endRange >= high)
        {
            segmentTree[pos] += delta;
            if(low != high) {
                lazy[2*pos + 1] += delta;
                lazy[2*pos + 2] += delta;
            }
            return;
        }

        int mid = (low + high)/2;
        updateSegmentTreeRangeLazy(segmentTree, lazy, startRange, endRange, delta, low, mid, 2*pos+1);
        updateSegmentTreeRangeLazy(segmentTree, lazy, startRange, endRange, delta, mid+1, high, 2*pos+2);
        segmentTree[pos] = Math.min(segmentTree[2*pos + 1], segmentTree[2*pos + 2]);
    }

    public int rangeMinimumQueryLazy(int segmentTree[], int lazy[], int qlow, int qhigh, int len)
    {
        return rangeMinimumQueryLazy(segmentTree, lazy, qlow, qhigh, 0, len - 1, 0);
    }

    private int rangeMinimumQueryLazy(int segmentTree[], int lazy[], int qlow, int qhigh, int low, int high, int pos)
    {
        if(low > high)
        {
            return Integer.MAX_VALUE;
        }
        if (lazy[pos] != 0)
        {
            segmentTree[pos] += lazy[pos];
            if (low != high)
            {
                lazy[2 * pos + 1] += lazy[pos];
                lazy[2 * pos + 2] += lazy[pos];
            }
            lazy[pos] = 0;
        }

        if(qlow > high || qhigh < low)
        {
            return Integer.MAX_VALUE;
        }

        if(qlow <= low && qhigh >= high)
        {
            return segmentTree[pos];
        }

        int mid = (low+high)/2;
        return Math.min(rangeMinimumQueryLazy(segmentTree, lazy, qlow, qhigh, low, mid, 2 * pos + 1), rangeMinimumQueryLazy(segmentTree, lazy,  qlow, qhigh, mid + 1, high, 2 * pos + 2));
    }
}