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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;
	private long ans = Long.MAX_VALUE;

	void solve() throws IOException {
		int[] a = nia(ni());
//		Helper.tr(a);
		long sum = 0;
		for (int i = 0; i < a.length; i++)
			sum += a[i];
		solve(a, 0, 4, sum, new long[4]);
		out.println(ans);
	}

	private void solve(int[] a, int i, int parts, long sum, long[] preSums) {
//		Helper.tr(i, parts, sum, preSums);
		if (parts == 1) {
			preSums[3] = sum;
//			Helper.tr("->", preSums);
			long min = Long.MAX_VALUE;
			long max = Long.MIN_VALUE;
			for (int j = 0; j < 4; j++) {
				min = Math.min(preSums[j], min);
				max = Math.max(preSums[j], max);
			}
			ans = Math.min(ans, max - min);
//			Helper.tr("->>", ans);
			return;
		}
		long s = 0;
		int j = i;
		while (j <= a.length - parts && (s + a[j]) * parts < sum) {
			s += a[j];
			j++;
		}
		preSums[4 - parts] = s;
		if (j > i)
			solve(a, j, parts - 1, sum - s, preSums);
		if (j < a.length - 1) {
			s += a[j];
			preSums[4 - parts] = s;
			solve(a, j + 1, parts - 1, sum - s, preSums);
			if (j + 1 < a.length - 1) {
				s += a[j + 1];
				preSums[4 - parts] = s;
				solve(a, j + 2, parts - 1, sum - s, preSums);
			}
		}

	}

	String ns() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine(), " ");
		}
		return tok.nextToken();
	}

	int ni() throws IOException {
		return Integer.parseInt(ns());
	}

	long nl() throws IOException {
		return Long.parseLong(ns());
	}

	double nd() throws IOException {
		return Double.parseDouble(ns());
	}

	String[] nsa(int n) throws IOException {
		String[] res = new String[n];
		for (int i = 0; i < n; i++) {
			res[i] = ns();
		}
		return res;
	}

	int[] nia(int n) throws IOException {
		int[] res = new int[n];
		for (int i = 0; i < n; i++) {
			res[i] = ni();
		}
		return res;
	}

	long[] nla(int n) throws IOException {
		long[] res = new long[n];
		for (int i = 0; i < n; i++) {
			res[i] = nl();
		}
		return res;
	}

	public static void main(String[] args) throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		tok = new StringTokenizer("");
		Main main = new Main();
		main.solve();
		out.close();
	}
}