You are given an array of n integer numbers a0, a1, ..., an - 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, ..., an - 1 (1 ≤ ai ≤ 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.

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
def solution():
    n = int(raw_input())
    arr = list(map(int, raw_input().split()))
    min_num = arr[0]
    min_dist = n
    idx = 0
    for i in range(n)[1:]:
        if arr[i] == min_num:
            if min_dist > i - idx:
                min_dist = i - idx
            idx = i
        elif arr[i] < min_num:
            min_num = arr[i]
            idx = i
            min_dist = n
    return min_dist


if __name__ == '__main__':
    print solution()
