Score : 600 points
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.
Input is given from Standard Input in the following format:
N A_1 A_2 ... A_N
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
5 3 2 4 1 2
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.
10 10 71 84 33 6 47 23 25 52 64
36
7 1 2 3 1000000000 4 5 6
999999994