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
#python3
#utf-8

n = int(input())
idx___val = [int(x) for x in input().split()]
minim = min(idx___val)
min_idxes = [idx for idx in range(n) if idx___val[idx] == minim]
min_dist = min([(min_idxes[i] - min_idxes[i - 1]) for i in range(1, len(min_idxes))])
print(min_dist)
