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: Wrong Answer)

#include<bits/stdc++.h>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>
using namespace::std;
namespace mp = boost::multiprecision;
typedef mp::number<mp::cpp_dec_float<32,int64_t>> cfloat;
typedef mp::cpp_int cint;
typedef long long lint;
typedef long double ldouble;
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
#define rep(i, n) for(lint i = 0; i < (lint)(n); i++)
#define irep(i) for(lint i = 0;; i++)
#define irep1(i) for(lint i = 1;; i++)
#define irep2(i) for(lint i = 2;; i++)
#define rrep(i, n) for(lint i = (lint)(n-1); i >-1; i--)
#define repi(i,a,b) for(lint i=lint(a);i<lint(b);i++)
#define rep2(i,a,b,c) for(lint i=lint(a);i>lint(b);i+=c)
#define all(x) (x).begin(),(x).end()
#define sl(c) (('a')<=(c)&&(c)<=('z'))
#define ll(c) (('A')<=(c)&&(c)<=('Z'))
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define PI 3.141592653589793
#define cout (cout<<fixed<<setprecision(15))
#define makeupper(t) (transform(all(t),t.begin(),::toupper))
#define makelower(t) (transform(all(t),t.begin(),::tolower))
#define dist(x1,y1,x2,y2) (pow(pow(x2-x1,2)+pow(y2-y1,2),0.5))
#define NEXT_LINE string junk; getline(cin, junk);
#define output(v) do{rep(i,v.size())cout<<(i?" ":"")<<v[i];cout<<"\n";}while(0)
#define output2(v) rep(i,v.size()){rep(j,v[i].size()){cout<<(j?" ":"")<<v[i][j];}cout<<"\n";}
#define SINF 1<<30
#define INF 9223372036854775807
#define MOD 1000000007
vector<lint> dx={-1,1,0,0,1,1,-1,-1};
vector<lint> dy={0,0,-1,1,1,-1,1,-1};
vector<lint> operator+(const vector<lint>& v1,const vector<lint>& v2){
    vector<lint> v(v1.size()+v2.size(),0);
    rep(i,v1.size())v[i]=v1[i];
    rep(i,v2.size())v[i+v1.size()]=v2[i];
    return v;
}
inline lint sum(vector<lint> v){
    lint sum=0;
    rep(i,v.size())sum+=v[i];
    return sum;
}
inline string replace(string str, string before, std::string after) {
	string::size_type  Pos(str.find(before));
	while (Pos != std::string::npos) {
		str.replace(Pos, before.length(), after);
		Pos = str.find(before, Pos + after.length());
	}
	return str;
}
inline vector<string> split(string s, string delim) {
	vector<string> elems;
	s=replace(s, "#", "HASH");
	s=replace(s, delim,"#");
	stringstream ss(s);
	string item;
	while (getline(ss, item, '#')) {
		elems.push_back(replace(item, "HASH", "#"));
	}
	return elems;
}
inline vector<int> cross(vector<int> a, vector<int> b) {
    return { a[1] * b[2] - a[2] * b[1],a[2] * b[0] - a[0] * b[2],a[0] * b[1] - a[1] * b[0] };
}
inline lint GCD(lint a,lint b){return b?GCD(b,a%b):a;}
inline vector<lint> primeList(lint n) {
    vector<bool> p(n+1);
    vector<lint> list;
    repi(i,1, n+1)p[i] = true;
    repi(i,2,sqrt(n)+1) {
        if (p[i]) {
            repi(j,2,n/i+1) {
                p[i*j] = false;
            }
        }
    }
    repi(i, 2, n+1)if (p[i])list.push_back(i);
    return list;
}
inline bool isPrime(int num){
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false;
    double sqrtNum = sqrt(num);
    for (int i = 3; i <= sqrtNum; i += 2){
        if (num % i == 0)return false;
    }
    return true;
}
inline lint max(vector<lint> num){
    lint M=num[0];
    rep(i,num.size())M=max(M,num[i]);
    return M;
}
inline lint min(vector<lint> num){
    lint M=num[0];
    rep(i,num.size())M=min(M,num[i]);
    return M;
}
inline lint signal(lint val){
    if(val==0)return 0;
    else return val/abs(val);
}
struct IVector2{
    lint x,y;
};
bool operator< (const IVector2 &s, const IVector2 &t){
        return s.x==t.x?s.y<t.y:s.x<t.x;
};
bool operator> (const IVector2 &s, const IVector2 &t){
        return s.x==t.x?s.y>t.y:s.x>t.x;
};
struct IVector3{
    lint x,y,z;
};
struct IVector4{
    lint x,y,z,w;
};
struct BIT{
    public:
    vector<lint> bit;
    lint n;
    BIT(lint _n){
        n=_n;
        bit.resize(n+1,0);
    }
    lint sum(lint i){
        if(!i)return 0;
        return bit[i]+sum(i-(i&-i));
    }
    void add(lint i,lint x){
        if(i>n)return;
        bit[i]+=x;
        add(i+(i&-i),x);
    }
    static lint inversion(vector<lint> v){
        lint tmp=min(v);
        rep(i,v.size())v[i]-=tmp-1;
        BIT b(max(v));
        lint ans = 0;
        rep(i,v.size()){
            ans+=i-b.sum(v[i]);
            b.add(v[i],1);
        }
        return ans;
    }
};
int main(int argc,char *argv[]){
    lint n;
    cin>>n;
    vector<lint> v(n),v2(n),v3(n);
    rep(i,n)cin>>v[i];
    rep(i,n)v2[i]=v[i];
    sort(all(v2));
    lint m=ceill((long double)n*(n-1)/4);
    lint k=n*(n-1)/2;
    lint left=-1;
    lint right=n;
    while(right-left>1){
        lint mid=left+(right-left)/2;
        rep(j,n)if(v[j]<v2[mid])v3[j]=-1;
        else v3[j]=1;
        repi(j,1,n)v3[j]+=v3[j-1];
        if(m>k-BIT::inversion(v3)){
            right=mid;
        }else{
            left=mid;
        }
    }
    cout<<v2[left];
}