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
import bisect

def list_output(s):    
    print(' '.join(map(str, s)))
    
def list_input(s='int'):
    if s == 'int':
        return list(map(int, input().split()))    
    elif s == 'float':
        return list(map(float, input().split()))
    return list(map(str, input().split()))

n = int(input())
a = list(map(int, input().split()))
amin = min(a)
pre = -1
res = int(1e9)
for i in range(n):
    if a[i] == amin:
        if pre > -1:
            res = min(res, i-pre)
        pre = i
print(res)
