Problem G. Greedy replacement ≡

Statement

Let we have array of integers a_i. You can select in it no more than one number and replace it to other. Cost of this replacement is absolute difference new and old numbers.

It is required to find replacement with a minimum cost, so that a pair of same elements appears in the array of prefix sums of this array.

Input format

First line of input data contains single number N — length of the array.

Second line contains the N integers a_i.

Output format

Output data must contains two integer numbers — index of element for replacement (starting by zero) and signed difference between new and old its values.

If there are many solutions, than output any from them.

Constraints

2 < N < 100000

|a_i| ≤ 10⁹

Sample tests

2
1 1

1 -1

3
1 2 -3

2 1