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
#!/usr/bin/env python

def main():
    n = int(input())
    a = [int(c) for c in input().split()]

    _min = min(a)

    pos = [i for i, e in enumerate(a) if e == _min]
    ans = len(a) - 1
    for i in range(1, len(pos)):
        cur = pos[i] - pos[i-1]
        if cur == 1:
            print(1)
            return
        
        if cur < ans:
            ans = cur

    print(ans)
        

if __name__ == '__main__':
    main()
