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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;
using namespace __gnu_pbds;

ll arr[100005],fq[100000],node[400005],ind[26],ind1[26],n,m;

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#include <bits/stdc++.h>
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;

int arr[305];
int vis[305];
int lvlarr[305];
vector <int> G[300];

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#include <bits/stdc++.h>
#define mx 1000005
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;

ll arr[mx],pre_sum[mx],n;
vector <ll> node[4*mx];

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#include <bits/stdc++.h>
#define mx 1000005
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;

ll cnt_zero[mx],n;
string arr;

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#include <bits/stdc++.h>
#define mx 1000005
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;

ll arr[mx],pre_sum[mx],n;
vector <ll> node[4*mx];

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#include <bits/stdc++.h>

using namespace std;

int arr[100005],node[400005];
void init(int i,int j,int n)
{
    if(i==j)
    {
        node[n]=arr[i];

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#include<bits/stdc++.h>
#define mx 10000000
using namespace std;

int node[4*mx+1],pos[mx+1],ans[mx+1];
unordered_set <int> sett;

void build()
{
    memset(node,-1,sizeof node);

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#include <bits/stdc++.h>
#define mx 30005
#define ll long long int
#define test_case printf("Case %d:\n",id++);

using namespace std;

int gin[mx+1],t,par[mx+1],level[mx+1],start[mx+1],endd[mx+1];
int sparse_table[21][mx+1],n;
ll tree[2*mx+5];

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#include <bits/stdc++.h>
#define ll long long int

using namespace std;

struct NODE
{
    int one,two,three,zero,cnt;
    NODE()
    {

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#include<bits/stdc++.h>

using namespace std;

#define ll long long
#define MAX 1000005

char box[2005][2005];
ll temp_row[205],n,m;