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 h(n, a):
    v=min(a)
    minx=n
    w=[]
    for i in range(0,n):
        if a[i]==v:
            w.append(i)
            if len(w)>=2:
                x=w[-1]
                y=w[-2]
                if x-y<minx:
                    minx=x-y
    return minx

n = input().strip()
a = input().strip().split()
a = list(map(int, a))
print(h(int(n), a))