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#include <bits/stdc++.h>
using namespace std;
typedef long double flt;
const flt eps = 1e-10;
const int MAXN = 100;
int sgn(flt x) {
if (x < -eps) return -1;
else return x > eps;
}
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
typedef pair<int, int> point;
const int MAXN=100000+10;
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
typedef long long LL;
const int MAXN=100000+10;
struct Point {
int x, y;
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
const int MAXN=20000+10;
const int MAXM=400000+10;
const int inf=100000000;
struct node {
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
const int MAXN=300+10;
const int inf=1e9;
struct Edge {
int v, cap;
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
typedef long long LL;
const int MAXN=1600+10;
const int SIZE=50;
const LL inf=1ll<<50ll;
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
const int MAXN=150+10;
const int MAXM=3000;
const int inf=1e9;
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
const int MAXN=800+10;
const int SIZE=25;
const int inf=1e9;
struct Edge {
#include <cmath>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <algorithm>
using namespace std;
const int MAXN=410;
const int inf=1e9;
#include <queue>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXN=610;
const int MAXM=80000;
const int inf=1e9;