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
if __name__ == '__main__':
    n = int(input())
    a = [int(i) for i in input().split()]
    mx, d = 0, 10**5 + 1

    for i in range(1, n):
        if a[i] < a[mx]:
            mx = i
            d = 10**5 + 1
            continue
        if a[i] == a[mx]:
            d = min(d, i - mx)
            mx = i
    print(d)