You are given an array of n integer numbers. Let sum(l, r) be the sum of all numbers on positions from l to r non-inclusive (l-th element is counted, r-th element is not counted). For indices l and r holds 0 ≤ l ≤ r ≤ n. Indices in array are numbered from 0.

For example, if a = [ - 5, 3, 9, 4], then sum(0, 1) = - 5, sum(0, 2) = - 2, sum(1, 4) = 16 and sum(i, i) = 0 for each i from 0 to 4.

Choose the indices of three delimiters delim₀, delim₁, delim₂ (0 ≤ delim₀ ≤ delim₁ ≤ delim₂ ≤ n) and divide the array in such a way that the value of res = sum(0, delim₀) - sum(delim₀, delim₁) + sum(delim₁, delim₂) - sum(delim₂, n) is maximal.

Note that some of the expressions sum(l, r) can correspond to empty segments (if l = r for some segment).

Input

The first line contains one integer number n (1 ≤ n ≤ 5000).

The second line contains n numbers a₀, a₁, ..., a_n - 1 ( - 10⁹ ≤ a_i ≤ 10⁹).

Output

Choose three indices so that the value of res is maximal. If there are multiple answers, print any of them.

Four Segments

Examples