Equal Cut

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.

Examples

Input

5 3 2 4 1 2

Output

2

Input

10 10 71 84 33 6 47 23 25 52 64

Output

36

Input

7 1 2 3 1000000000 4 5 6

Output

999999994

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

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

Examples

Input

5 3 2 4 1 2

Output

2

Input

10 10 71 84 33 6 47 23 25 52 64

Output

36

Input

7 1 2 3 1000000000 4 5 6

Output

999999994

样例

10
10 71 84 33 6 47 23 25 52 64

36