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#include <bits/stdc++.h>
#define mxs 100005
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long int
#define print_case printf("Case %lld: ",ts++)
using namespace std;
int arr[3005],brr[300005],n,m,cnt;
#include <bits/stdc++.h>
#define mxs 100005
#define ll long long int
#define print_case printf("Case %lld: ",ts++)
using namespace std;
ll arr[100005],n,m,cnt;
ll qube[21][21][21],cum[21][21][21],sum[21];
#include <bits/stdc++.h>
#define mxs 100005
#define ll long long int
#define print_case printf("Case %lld: ",ts++)
using namespace std;
ll arr[100005],n,m,cnt;
vector <string> svc;
string str;
#include <bits/stdc++.h>
#define mxs 100005
#define ll long long int
using namespace std;
int arr[100005],n,m;
ll node[100005];
pair <int,int> pi[100005];
ll query(int ind)
#include <bits/stdc++.h>
using namespace std;
struct nn
{
int lazy,cnt;
nn()
{
lazy=0;
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
ordered_set sett;
#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[100005],ind[26],ind1[26],n,m;
#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[100005],ind[26],ind1[26],n,m;
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp> // Common file
#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[1000000],fq[1000000],dp[1000000],ind[26],ind1[26],n,m;
#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;