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
#problem 911
#6.01.2018
def main():
    n=int(input())
    a=list(map(int,input().split()))
    c=[]
    min_number=min(a)
    min_index=n
    for i in range(n):
        if a[i]==min_number:
            c.append(i)

    for i in range(1,len(c)):
        min_index=min((c[i]-c[i-1]),min_index)

    print(min_index)

if __name__=='__main__':
    main()
