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
from sys import maxsize
n = int(input())
arr = list(map(int,input().split()))
m = maxsize
res= maxsize
ind = []
for i in range(len(arr)):
    if arr[i] < m:
        m = arr[i]
        ind = [i]
        res=maxsize
    elif arr[i] == m:
        ind.append(i)
        if ind[-1]-ind[-2] < res and len(ind) > 1:
            res = ind[-1]-ind[-2]
print(res)
