You are given an array A consisting of N numbers. In one move you can delete either the first two, the last two, or the first and last elements of A. No move can be performed if the length of A is smaller than 2. The result of each move is the sum of the deleted elements.
Given an array A of N integers, returns the maximum number of moves that can be performed on A, such that all performed moves have the same result.
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Example 1:
Input: A = [3, 1, 5, 3, 3, 4, 2]
Output: 3
Explanation:The first move should delete two last elements (4 and 2 with sum = 6), then A = [3, 1, 5, 3, 3]. The second move may delete first and last elements (3 and 3 with sum = 6), then A = [1, 5, 3]. The third move should delete first two elements (1 and 5 with sum = 6), then A = [3].
Example 2:
Input: A = [4, 1, 4, 3, 3, 2, 5, 2]
Output: 4
Explanation:It is possible to delete the first and last elements four times, as each such pair of elements sums up to 6.
Example 3:
Input: A = [1, 9, 1, 1, 1, 1, 1, 1, 8, 1]
Output: 1
Explanation:There is no way to perform move that results with the same sum more than once.
Example 4:
Input: A = [1, 9, 8, 9, 5, 1, 2]
Output: 3
Explanation:The first move should delete the first two elements, then the second and third moves should delete first and last elements twice.
Example 5:
Input: A = [1, 1, 2, 3, 1, 2, 2, 1, 1, 2]
Output: 4
Explanation:One of the possible sequence of moves goes as follows: twice delete the last two elements, then delete the first and last elements, last move deletes the first two elements.
- N is an integer within the range [1..1,000];
- each element of array A is an integer within the range [1..1,000,000,000].
input:
output: