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 get_ints():
    return list(map(int, input().split()))

N = int(input())
a = get_ints()

ans = 2e9
pos = 0
curr = a[0]
for i in range(1,N):
    if a[i]<curr:
        curr = a[i]
        ans = 1e9
        pos = i
    elif a[i]==curr:
        ans = min(ans,i-pos)
        pos = i
print(ans)