You are given an array of n integer numbers a0, a1, ..., a**n - 1. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times.

Input

The first line contains positive integer n (2 ≤ n ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., a**n - 1 (1 ≤ a**i ≤ 109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

Output

Print the only number — distance between two nearest minimums in the array.

Samples

2
3 3

1

3
5 6 5

2

9
2 1 3 5 4 1 2 3 1

3