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

n = input()
arr = [[v, i] for i,v in enumerate(list(map(int, input().strip().split())))]
arr.sort()
x = arr[0][0]
i = 0
ans = 10**20
while i+1<len(arr) and arr[i+1][0] == x:
    ans = min(ans, abs(arr[i+1][1]-arr[i][1]))
    i += 1
print(ans)