Problem:
Score : 700 points

Problem Statement

We will define the median of a sequence b of length M, as follows:

Let b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.

For example, the median of (10, 30, 20) is 20; the median of (10, 30, 20, 40) is 30; the median of (10, 10, 10, 20, 30) is 10.

Snuke comes up with the following problem.

You are given a sequence a of length N.
For each pair (l, r) (1 \leq l \leq r \leq N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, ..., a_r) of a.
We will list m_{l, r} for all pairs (l, r) to create a new sequence m.
Find the median of m.

Constraints

1 \leq N \leq 10^5

a_i is an integer.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the median of m.

Sample Input 1

3
10 30 20

Sample Output 1

30

The median of each contiguous subsequence of a is as follows:

The median of (10) is 10.

The median of (30) is 30.

The median of (20) is 20.

The median of (10, 30) is 30.

The median of (30, 20) is 30.

The median of (10, 30, 20) is 20.

Thus, m = (10, 30, 20, 30, 30, 20) and the median of m is 30.

Sample Input 2

1
10

Sample Output 2

10

Sample Input 3

10
5 9 5 9 8 9 3 5 4 3

Sample Output 3

8

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <algorithm>
#include <iostream>
#include <vector>
#include <assert.h>
#include <map>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <math.h>
#include <string>
#include <string.h>
#include <queue>
#include <complex>
#include <iomanip>
#include <stack>
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
ll mod=1e9+7;
double eps=1e-7;
ll exp(ll x,ll y){if(y<0) return 0; ll ret=1;for(;y;y>>=1,x=(x*x)%mod){if(y&1)ret=(ret*x)%mod;}return ret;}
ull pexp(ull x,ull y){if(y<0) return 0; ull ret=1; for(;y;y>>=1,x=(x*x)){if(y&1)ret=(ret*x);}return ret;}
ll gcd(ll x,ll y){if(!x||!y) return x+y; return x%y==0?y:gcd(y,x%y);}
ll lcm(ll x,ll y){return x*(y/gcd(x,y));}
ll bsum(ll u,ll b){ll ret=0;if(u<b)return u;while(u){ret+=u%b;u/=b;}return ret;}
ll prival(ll u,ll p){ll cn=0;while(u%p==0){cn++;u=u/p;}return cn;}
ll minv(ll a,ll b){return 1<a?b-minv(b%a,a)*b/a:1;}
ll extm(ll a,ll b){ll ret=0;while(a!=0){if(a%2==1){ret+=b;ret%=mod;}a>>=1;b=(2*b)%mod;}return ret;}   
ll eaphi(ll x){ll t=x,ret=x,i;for(i=2;i*i<=x;i++){if(t%i==0){ret-=ret/i;while(t%i==0) t/=i;}}if(t!=1) ret-=ret/t;return ret;}
ll eadivc(ll x){ll ret=0;ll i;for(i=1;i*i<=x;i++){if(x%i==0 && i*i!=x) ret+=2;if(x%i==0 && i*i==x) ret+=1;}return ret;}
ll eadivs(ll x){ll ret=0;ll i;for(i=1;i*i<=x;i++){if(x%i==0 && i*i!=x) ret+=i+x/i;if(x%i==0 && i*i==x) ret+=i;}return ret;}
ll ndig(ll x, ll b){ll ret=0;while(x){x/=b; ret++;}return ret;}
ll rev(ll n, ll b){ll ret=0;while(n){ret=b*ret+n%b; n/=b;}return ret;}
ll sq(ll x){ll t=(ll)sqrt(x); for(ll i=t-2 ; i<=t+2 ; i++) if(i*i==x) return abs(i); return -1;}
ll extexp(ll x,ll y){if(y<0) return 0; ll ret=1;for(;y;y>>=1,x=extm(x,x)){if(y&1)ret=extm(ret,x);}return ret;}
bool isprime(ll x){if(x<=1) return false; for(ll i=2;i*i<=x;i++){if(x%i==0){return false;}}return true;}
ll vv[111111];
ll fin[111111];
ll ps[111111];
ll tree[444444];
ll lef, rig, mid, best, n, C;

ll query(ll l, ll r)
{
	ll ret=0;
	for(l+=C , r+=C ; l<r ; l>>=1, r>>=1)
	{
		if(l&1) ret+=tree[l++];
		if(r&1) ret+=tree[--r];
	}
	return ret;
}

void upd(ll loc, ll val)
{
	loc+=C; tree[loc]+=val;
	for( ; loc>1 ; loc>>=1) tree[loc>>1]=tree[loc]+tree[loc^1];
}

bool isok(ll x) // m_{l,r}>=x인 #[l,r] * 2 >= (n+1)C2
{
	int i; ll ret=0; C=2*n+4;
	for(i=0 ; i<=444400 ; i++) tree[i]=0;
	for(i=0 ; i<=n ; i++) ps[i]=0;
	for(i=1 ; i<=n ; i++)
	{
		if(vv[i]>=x) fin[i]=1;
		else fin[i]=-1; 
	}
	for(i=1 ; i<=n ; i++) ps[i]=ps[i-1]+fin[i];
	for(i=0 ; i<=n ; i++) ps[i]+=n;
	for(i=0 ; i<=n ; i++)
	{
		ret+=query(0,ps[i]+1);
		upd(ps[i],1);
	}
	if(2*ret>=(n+1)*n/2) return true;
	return false;
}

int main(void)
{
	ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	cin>>n; int i;
	for(i=1 ; i<=n ; i++) cin>>vv[i];
	lef=1; rig=1e9+7;
	while(lef<=rig)
	{
		mid=(lef+rig)/2;
		if(isok(mid)) best=mid, lef=mid+1;
		else rig=mid-1;
	}
	cout<<best; return 0;
}



// 제출하기 전에 생각햇나요?
// it may be easier/harder than you think
// ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);