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#include <queue>
#include <tuple>
#include <cstring>
#include <iostream>
using namespace std;
int mat[50][50];
int group[50][50];
#include <tuple>
#include <queue>
#include <string>
#include <vector>
#include <utility>
#include <iostream>
#include <algorithm>
using namespace std;
#include <queue>
#include <vector>
#include <cstring>
#include <utility>
#include <iostream>
using namespace std;
int n, m;
int mat[20][20];
#include <string>
#include <iostream>
using namespace std;
int main(void) {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
string a, b;
#include <vector>
#include <iostream>
using namespace std;
int check[20001];
vector<int> mat[20001];
bool go(int idx, int val) {
check[idx] = val;
#include <queue>
#include <deque>
#include <tuple>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
using namespace std;
#include <vector>
#include <iostream>
using namespace std;
bool visit[1001];
vector<int> a[1001];
void go(int idx) {
if (visit[idx]) {
#include <queue>
#include <tuple>
#include <deque>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int n;
vector<char> vc;
struct Base {
#include <vector>
#include <cstring>
#include <iostream>
using namespace std;
int n;
vector<char> vc;
bool visit[10];