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: Time Limit Exceeded)

#include<bits/stdc++.h>
#define fr(i,n) for(int i=0;i<(n);++i)
#define foor(i,a,b) for(int i=(a);i<=(b);++i)
#define rf(i,n) for(int i=(n);i--;)
#define roof(i,b,a) for(int i=(b);i>=(a);--i)
#define elsif else if
#define all(x) x.begin(),x.end()
#define Sort(x) sort(all(x))
#define Reverse(x) reverse(all(x))
#define PQ priority_queue
#define NP(x) next_permutation(all(x))
using namespace std;            typedef vector<bool> vb; typedef vector<vb>  vvb;
                                typedef vector<int>  vi; typedef vector<vi>  vvi;
typedef long long ll;           typedef vector< ll>  vl; typedef vector<vl>  vvl;
typedef unsigned long long ull; typedef vector<ull>  vu; typedef vector<vu>  vvu;
typedef double dbl;             typedef vector<dbl>  vd; typedef vector<vd>  vvd;
typedef string str;             typedef vector<str>  vs; typedef vector<vs>  vvs;
typedef pair<int,int>pii;       typedef vector<pii>vpii; typedef map<int,int>mii;
typedef pair< ll, ll>pll;       typedef vector<pll>vpll; typedef map< ll, ll>mll;
typedef pair<dbl,dbl>pdd;       typedef vector<pdd>vpdd; typedef map<dbl,dbl>mdd;
typedef pair<str,str>pss;       typedef vector<pss>vpss; typedef map<str,str>mss;
typedef pair<int, ll>pil;       typedef vector<pil>vpil; typedef map<int, ll>mil;
typedef pair< ll,int>pli;       typedef vector<pli>vpli; typedef map< ll,int>mli;
typedef pair<dbl,int>pdi;       typedef vector<pdi>vpdi; typedef map<dbl,int>mdi;
template<typename T>vector<T>&operator<<(vector<T>&v,const T t){v.push_back(t);return v;}
template<typename T>multiset<T>&operator<<(multiset<T>&m,const T t){m.insert(t);return m;}
template<typename T>set<T>&operator<<(set<T>&s,const T t){s.insert(t);return s;}
template<typename T,typename U>PQ<T,vector<T>,U>&operator<<(PQ<T,vector<T>,U>&q,const T t){q.push(t);return q;}
template<typename T,typename U>istream&operator>>(istream&s,pair<T,U>&p){return s>>p.first>>p.second;}
template<typename T>istream&operator>>(istream&s,vector<T>&v){fr(i,v.size()){s>>v[i];}return s;}
template<typename T,typename U>ostream&operator<<(ostream&s,const pair<T,U>p){return s<<p.first<<" "<<p.second;}
template<typename T>ostream&operator<<(ostream&s,const vector<T>v){for(auto a:v){s<<a<<endl;}return s;}
template<typename T,typename U>pair<T,U>operator+(pair<T,U>a,pair<T,U>b){return {a.first+b.first,a.second+b.second};}
template<typename T,typename U>pair<T,U>operator-(pair<T,U>a,pair<T,U>b){return {a.first-b.first,a.second-b.second};}
template<typename T>void print(T x){cout<<x<<endl;}
const int MD=1e9+7;
template<typename T>str to_string(const T&n){ostringstream s;s<<n;return s.str();}
template<typename T,typename U>vector<pair<T,U>>dijkstra(const vector<vector<pair<T,U>>>E,const U s,const T inf){using P=pair<T,U>;vector<P>d;fr(i,E.size()){d<<P{inf,i};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
template<typename T,typename U>map<U,pair<T,U>>dijkstra(map<U,vector<pair<T,U>>>E,const U s,const T inf){using P=pair<T,U>;map<U,P>d;for(pair<U,vector<P>>e:E){d[e.first]=P{inf,e.first};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
template<typename T>T distsq(pair<T,T>a,pair<T,T>b){return (a.first-b.first)*(a.first-b.first)+(a.second-b.second)*(a.second-b.second);}
template<typename T>T max(const vector<T>a){T m=a[0];for(T e:a){m=max(m,e);}return m;}
template<typename T>T min(const vector<T>a){T m=a[0];for(T e:a){m=min(m,e);}return m;}
template<typename T>T gcd(const T a,const T b){return a?gcd(b%a,a):b;}
template<typename T>T gcd(const vector<T>a){T g=a[0];for(T e:a){g=gcd(g,e);}return g;}
template<typename T>vector<T>LIS(const vector<T>A){vi B;for(T a:A){auto it=lower_bound(all(B),a);if(it==B.end()){B<<a;}else{*it=a;}}return B;}
ll strmod(const str&s,const int m){ll x=0;fr(i,s.size()){x=(x*10+s[i]-48)%m;}return x;}
vvl mul(const vvl&A,const vvl&B,const int m){vvl C;fr(y,A.size()){C<<vl(B[y].size());}fr(y,C.size()){fr(x,C[y].size()){fr(i,A[0].size()){(C[y][x]+=A[y][i]*B[i][x])%=m;}}}return C;}
vvl pow(const vvl&A,const ll n,const int m){vvl B;fr(y,A.size()){B<<vl(A.size());}if(n==0){fr(i,B.size()){B[i][i]=1;}}elsif(n%2){B=mul(A,pow(A,n-1,m),m);}else{vvl C=pow(A,n/2,m);B=mul(C,C,m);}return B;}
ll pow(const ll a,const ll n,const int m){ll t;return n?(n&1?a>=0?a%m:~-m+~a%m:1)*(t=pow(a,n>>1,m),t*t%m)%m:!!a;}
ll inv(const ll x,const int p){return pow(x,p-2,p);}
vpll fact(const int n,const int p){vpll v(n+1);v[0].first=1;foor(i,1,n){v[i].first=v[i-1].first*i%p;}v[n].second=inv(v[n].first,p);roof(i,n,1){v[i-1].second=v[i].second*i%p;}return v;}
ll C2(const int n){return(ll)n*~-n/2;}
ll sum(const vi a){ll s=0;for(int e:a){s+=e;}return s;}
ll sum(const vl a){ll s=0;for(ll e:a){s+=e;}return s;}
ll segsum(vl&s,int l,int r){l|=s.size()>>1;r|=s.size()>>1;if(l==r){return s[l];}ll z=s[l]+s[r];for(;l>>1<r>>1;l>>=1,r>>=1){l&1||(z+=s[l^1]);r&1&&(z+=s[r^1]);}return z;}
void segadd(vl&s,int i,ll x){s[i|=s.size()>>1]+=x;for(;i>>1>=1;i>>=1){s[i>>1]=s[i]+s[i^1];}}
ll fib(const ll n,const int m){ll a,b,c,d,A,B,C,D;a=1;b=0;c=0;d=1;rf(i,63){A=a*a+b*c;B=a*b+b*d;C=c*a+d*c;D=c*b+d*d;if(n>>i&1){a=A;b=B;c=C;d=D;A=a+b;B=a;C=c+d;D=c;}a=A%m;b=B%m;c=C%m;d=D%m;}return b;}
vi primes(int n){vb b(n+1);vi p;foor(i,2,n){if(!b[i]){p<<i;for(int j=2*i;j<=n;j+=i){b[j]=true;}}}return p;}
// (int) * (int) => (int)
// (int) / (int) => (int)

ll BITsum(vl&B,int i){
	ll z=0;
	while(i>0){
		z+=B[i];
		i-=i&-i;
	}
	return z;
}

void BITadd(vl&B,int i,ll x){
	while(i<B.size()){
		B[i]+=x;
		i+=i&-i;
	}
}

int main(){cin.tie(0);ios::sync_with_stdio(false);
	int N;
	cin>>N;
	vi A(N);
	cin>>A;
	int z=0;
	rf(k,30){
		int K=z|1<<k;
		vi B(N+1);
		fr(i,N){
			B[i+1]=B[i]+(A[i]>=K?1:-1);
		}
		mli m;
		fr(i,N+1){
			m[B[i]]=0;
		}
		{
			int i=0;
			for(pli e:m){
				m[e.first]=++i;
			}
		}
		vl S(1<<17);
		ll x=0;
		fr(i,N+1){
			x+=BITsum(S,m[B[i]]);
			BITadd(S,m[B[i]],1);
		}
		if(x>=(C2(N+1)+1)/2){
			z=K;
		}
	}
	print(z);
	return 0;
}