Problem:
Score : 600 points

Problem Statement

Snuke has an integer sequence A of length N.

He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.
The positions of the cuts can be freely chosen.

Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively.
Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller.
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.

Constraints

4 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.

Sample Input 1

5
3 2 4 1 2

Sample Output 1

2

If we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.
Here, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.
We cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.

Sample Input 2

10
10 71 84 33 6 47 23 25 52 64

Sample Output 2

36

Sample Input 3

7
1 2 3 1000000000 4 5 6

Sample Output 3

999999994

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

#include <iostream>
#include <string>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <complex>
#include <utility>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <bitset>
#include <ctime>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <cassert>
#include <cstddef>
#include <iomanip>
#include <numeric>
#include <tuple>
#include <sstream>
#include <fstream>

using namespace std;
#define REP(i, n) for (int (i) = 0; (i) < (n); (i)++)
#define FOR(i, a, b) for (int (i) = (a); (i) < (b); (i)++)
#define RREP(i, a) for(int (i) = (a) - 1; (i) >= 0; (i)--)
#define FORR(i, a, b) for(int (i) = (a) - 1; (i) >= (b); (i)--)
#define DEBUG(C) cerr << #C << " = " << C << endl;
using LL = long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<LL>;
using VVL = vector<VL>;
using VD = vector<double>;
using VVD = vector<VD>;
using PII = pair<int, int>;
using PDD = pair<double, double>;
using PLL = pair<LL, LL>;
using VPII = vector<PII>;
template<typename T> using VT = vector<T>;
#define ALL(a) begin((a)), end((a))
#define RALL(a) rbegin((a)), rend((a))
#define SORT(a) sort(ALL((a)))
#define RSORT(a) sort(RALL((a)))
#define REVERSE(a) reverse(ALL((a)))
#define MP make_pair
#define FORE(a, b) for (auto &&a : (b))
#define FIND(s, e) ((s).find(e) != (s).end())
#define EB emplace_back
template<typename T> inline bool chmax(T &a, T b){if (a < b){a = b;return true;}return false;}
template<typename T> inline bool chmin(T &a, T b){if (a > b){a = b;return true;}return false;}

const int INF = 1e9;
const int MOD = INF + 7;
const LL LLINF = 1e18;

const int MAX = 2e5 + 10;
int N;
LL A[MAX];

LL get(int l, int r) {
    // [l, r)
    //cerr << l << " " << r << endl;
    //cerr << A[r] - A[l] << endl;
    return A[r] - A[l];
}

int main(void) {
    cin >> N;
    REP(i, N) cin >> A[i + 1];
    REP(i, N) A[i + 1] += A[i];
    LL ans = LLINF;
    FOR(i, 2, N - 1) {
        VT<PLL> l, r;
        {
            int low = 1, high = i;
            while (high - low > 1) {
                const int mid = (low + high) >> 1;
                if (get(mid, i) - get(0, mid) >= 0) {
                    high = mid;
                } else {
                    low = mid;
                }
            }
            FOR(j, low - 2, low + 3) {
                if (0 < j && j < i) l.EB(get(0, j), get(j, i));
            }
        }
        {
            int low = i + 1, high = N;
            while (high - low > 1) {
                const int mid = (low + high) >> 1;
                if (get(mid, N) - get(i, mid) >= 0) {
                    high = mid;
                } else {
                    low = mid;
                }
            }
            FOR(j, low - 2, low + 3) {
                if (i < j && j < N) r.EB(get(i, j), get(j, N));
            }
        }
        FORE(le, l) FORE(re, r) {
            VL vec;
            vec.EB(le.first);
            vec.EB(le.second);
            vec.EB(re.first);
            vec.EB(re.second);
            SORT(vec);
            chmin(ans, vec.back() - vec.front());
        }
    }
    cout << ans << endl;
}