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#include<bits/stdc++.h>
#define mx 100005
#define test_case printf("Case %d:\n",id++)

using namespace std;

int arr[mx+1],node[4*mx+1],first_pos[mx+1],freq[mx+1];

unordered_map <int,int> unmap;

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#include<bits/stdc++.h>
#define mx 200005
using namespace std;

int arr[mx+1],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>

using namespace std;

struct nn
{
    int sum,prop;
    nn()
    {
        sum=0;

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

using namespace std;

struct NODE
{
    ll pop,sum;
}node[400005];

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#include<bits/stdc++.h>

#define N 1000000

using namespace std;

struct st
{
    int zero,one,two,cnt;
    st()

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#include<bits/stdc++.h>
#define mx 200005
#define ll long long int
#define test_case printf("Case %d:",id++)

using namespace std;

ll arr[mx+1],node[mx+1],n;

vector <pair <ll,ll> > vc;

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

using namespace std;

int arr[100005];

int main() {
    int i,j,k,l,m,n,s,e,v,key,x,t,c=1;
    cin>>t;

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#include<bits/stdc++.h>

using namespace std;

#define ll long long
#define MAX 1000005

char box[2001][2001];
ll temp_row[30000],n,m;

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

using namespace std;

int arr[100005],node[100005],n;

void update(int ind,int val)
{
    for(int i=ind;i<=n;i+=(i&-i))

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#include <bits/stdc++.h>
#define ll long long int
 
using namespace std;
 
struct NODE
{
    ll pop,sum;
}node[400005];