/*
__----~~~~~~~~~~~------___
. . ~~//====...... __--~ ~~
-. \_|// |||\\ ~~~~~~::::... /~
___-==_ _-~o~ \/ ||| \\ _/~~-
__---~~~.==~||\=_ -_--~/_-~|- |\\ \\ _/~
_-~~ .=~ | \\-_ '-~7 /- / || \ /
.~ .~ | \\ -_ / /- / || \ /
/ ____ / | \\ ~-_/ /|- _/ .|| \ /
|~~ ~~|--~~~~--_ \ ~==-/ | \~--===~~ .\
' ~-| /| |-~\~~ __--~~
|-~~-_/ | | ~\_ _-~ /\
/ \ \__ \/~ \__
_--~ _/ | .-~~____--~-/ ~~==.
((->/~ '.|||' -_| ~~-/ , . _||
-_ ~\ ~~---l__i__i__i--~~_/
_-~-__ ~) \--______________--~~
//.-~~~-~_--~- |-------~~~~~~~~
//.-~~~--\
*/
#define _CRT_SECURE_NO_WARNINGS
#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<bitset>
#include<cassert>
#include<cctype>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<deque>
#include<iomanip>
#include<list>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>
#define lt k << 1
#define rt k << 1 | 1
#define lowbit(x) x & (-x)
#define lson l, mid, lt
#define rson mid+1, r, rt
using namespace std;
typedef long long ll;
typedef long double ld;
#define fin freopen("in.txt", "r", stdin);
#define fout freopen("out.txt", "w", stdout);
#define ios ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define mem(a, b) memset(a, b, sizeof(a))
//#define int ll
const double pi = acos(-1.0);
const double eps = 1e-8;
const ll mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int maxn = 2e5 + 500;
