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#include <iostream>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i, j, k) for(int i = j; i < k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)
typedef unsigned long long ull;
#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define FOR(i, j, k) for(int i = j; i < (int)k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)
typedef unsigned long long ull;
#include <iostream>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <utility>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define FOR(i, j, k) for(int i = j; i < (int)k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)
typedef unsigned long long ull;
#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define FOR(i, j, k) for(int i = j; i < (int)k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)
typedef unsigned long long ull;
#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define FOR(i, j, k) for(int i = j; i < (int)k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)
typedef unsigned long long ull;