You are given an array of n integer numbers a_0, a_1, ..., 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 ≤ 10^5) — size of the given array. The second line contains n integers a_0, a_1, ..., a_{n} - 1 (1 ≤ a_{i} ≤ 10^9) — 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.

-----Examples-----

Input 2 3 3

Output 1

Input 3 5 6 5

Output 2

Input 9 2 1 3 5 4 1 2 3 1

Output 3