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 Python (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
def two_pointers(ary, l, r, split, ary_func, comb_func, comp_func):
    '''
    This function is supposed to be repeatedly called so that 'split' keeps
    renewing, under an assumption that 'split' increases monotonously.
    ('l' and 'r' just specify the region to be searched in 'ary')
    '''

    left = ary_func(ary, l, split)
    right = ary_func(ary, split, r)
    val = comb_func(left, right)

    for i in range(split + 1, r):
        tmp_left = ary_func(ary, l, i)
        tmp_right = ary_func(ary, i, r)
        tmp_val = comb_func(tmp_left, tmp_right)

        if comp_func(val, tmp_val):
            return i - 1, val, left, right
        else:
            left = tmp_left
            right = tmp_right
            val = tmp_val

    else:
        return r - 1, val, left, right


if __name__ == '__main__':
    from operator import add
    from itertools import accumulate

    n = int(input())
    a = [int(_) for _ in input().split()]
    cul_ary = [0] + list(accumulate(a, add))

    l_split = 1
    r_split = 3
    griefs = []
    for i in range(2, n - 1):
        # left
        l_split, l_diff, p, q = two_pointers(cul_ary,
                                             0,
                                             i,
                                             l_split,
                                             lambda ary, l, r: ary[r] - ary[l],
                                             lambda left, right: abs(left - right),
                                             lambda val1, val2: True if val1 < val2 else False)

        # right
        r_split, r_diff, r, s = two_pointers(cul_ary,
                                             i,
                                             n,
                                             r_split,
                                             lambda ary, l, r: ary[r] - ary[l],
                                             lambda left, right: abs(left - right),
                                             lambda val1, val2: True if val1 < val2 else False)

        griefs.append(max(p, q, r, s) - min(p, q, r, s))

    print(min(griefs))