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#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,a,b) for(int i=(a);i<(b);i++)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()
#include<bits/stdc++.h>
using namespace std;
int extgcd(int a,int b,int &x,int &y){
if(b==0){ //a*1+b*0=a なので!
x=1;
y=0;
return a;
}
template<class T>
vector<int>construct_sa(const T &s){
int n=s.size();
vector<int>r(n+1),sa(n+1);
rep(i,n)r[i]=s[i];
r[n]=-1;
iota(all(sa),0);
sort(all(sa),[&](int a,int b){
return r[a]<r[b];
});
# Your init script
#
# Atom will evaluate this file each time a new window is opened. It is run
# after packages are loaded/activated and after the previous editor state
# has been restored.
#
# An example hack to log to the console when each text editor is saved.
#
# atom.workspace.observeTextEditors (editor) ->
# editor.onDidSave ->
#include<bits/stdc++.h>
using namespace std;
#define int long long
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,f,n) for(int i=(f);i<(n);i++)
#define all(v) (v).begin(),(v).end()
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef complex<int> Point;
bool Comp(const Point &p, const Point &q)
{
if (p.real() != q.real()) return p.real() < q.real();
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;