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 $P,Q,R,S$.