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#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <iostream>
#include <cstring>
#include <vector>
#include <fstream>
#include <map>
#include <set>
#include <stack>
#include <cstdio>
#include <iostream>
#include <cmath>
#include <cstring>
#include <cctype>
#include <algorithm>
#define sd(a) scanf("%d",&a)
#define sdd(a,b) scanf("%d%d",&a,&b)
#define abs(x) (x>0?x:(0-x))
#define MAX(a,b) (a>b?a:b)