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#include <bits/stdc++.h>
#define REP(i, a, b) for (int i = a; i <= b; i++)
#define FOR(i, n) for (int i = 0; i < n; i++)
#define foreach(it, ar) for ( typeof(ar.begin()) it = ar.begin(); it != ar.end(); it++ )
#define PI 3.1415926535897932385
#define uint64 unsigned long long
#define Int long long
#define int64 long long
#include <bits/stdc++.h>
using namespace std ;
map<int,string> m ;
double processor_unit_time ;
double observed_time ;
const int MAXN = 1e6 ;
vector<int>a( MAXN ) ;
#define FOR(i, n) for (int i = 0; i < n; i++)
#include<bits/stdc++.h>
using namespace std;
/* When Panda is Life !
_,add8ba,
,d888888888b,
d8888888888888b _,ad8ba,_
d888888888888888) ,d888888888b,
I8888888888888888 _________ ,8888888888888b
__________`Y88888888888888P"""""""""""baaa,__ ,888888888888888,
/** Code For Dynamic Huffman **/
#include <bits/stdc++.h>
#define Int long long
#define REP(i, a, b) for (int i = a; i <= b; i++)
#define FOR(i, n) for (int i = 0; i < n; i++)
#define foreach(it, ar) for ( typeof(ar.begin()) it = ar.begin(); it != ar.end(); it++ )
#define PI 3.1415926535897932385
/*
PROJECT FOR THE END-SEM
COMPLEXITY ANALYSIS OF AN ALGORITHM BASEDON DIFFERENT TEST CASES
1 ) BASIC IDEA : AN ALGORITHM WOULD BE TESTED ON VARIOUS TEST CASES BASED ON DIFFERENT INPUT SIZES
*/
#include <bits/stdc++.h>
using namespace std ;
map<int,string> m ;
#include<bits/stdc++.h>
#define ll long long
using namespace std;
vector<int> w;
vector<ll int> h;
ll int c[5010][5010];
ll int dp[2][5010];
void f(int g,int l1,int l2,int p1,int p2)
{
if(l1>l2)
#include <bits/stdc++.h>
using namespace std;
/* When Panda is Life !
_,add8ba,
,d888888888b,
d8888888888888b _,ad8ba,_
d888888888888888) ,d888888888b,
/* When Panda is Life !
_,add8ba,
,d888888888b,
d8888888888888b _,ad8ba,_
d888888888888888) ,d888888888b,
I8888888888888888 _________ ,8888888888888b
__________`Y88888888888888P"""""""""""baaa,__ ,888888888888888,
,adP"""""""""""9888888888P""^ ^""Y8888888888888888I
,a8"^ ,d888P"888P^ ^"Y8888888888P'
/* When Panda is Life !
_,add8ba,
,d888888888b,
d8888888888888b _,ad8ba,_
d888888888888888) ,d888888888b,
I8888888888888888 _________ ,8888888888888b
__________`Y88888888888888P"""""""""""baaa,__ ,888888888888888,
,adP"""""""""""9888888888P""^ ^""Y8888888888888888I
,a8"^ ,d888P"888P^ ^"Y8888888888P'
/* When Panda is Life !
_,add8ba,
,d888888888b,
d8888888888888b _,ad8ba,_
d888888888888888) ,d888888888b,
I8888888888888888 _________ ,8888888888888b
__________`Y88888888888888P"""""""""""baaa,__ ,888888888888888,
,adP"""""""""""9888888888P""^ ^""Y8888888888888888I
,a8"^ ,d888P"888P^ ^"Y8888888888P'