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
# mz
# feb2, 2018

def main():
    n = int(input())
    l = list(map(lambda x: int(x), input().split()))
    minimum = sorted(l)[0]

    idx = []
    i = 0
    for i in range(n):
        if l[i] == minimum:
            idx.append(i)
            i += 1

    res = sorted(list(map(lambda x: minus(*x), list(zip(idx[1:], idx[0:-1])))))[0]
    print(res)

def minus(x,y):
    return x - y

if __name__ == '__main__':
    main()
