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 main():
    input()
    arr=list(map(int,input().split()))
    k=min(arr)
    ak=[]
    for i in range(len(arr)):
        if(arr[i]==k): ak.append(i)
    ak.sort()
    r=len(arr)
    for i in range(len(ak)-1):
        r=min(r,ak[i+1]-ak[i])
    return r
 
print(main())