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
#!/bin/python3
import sys

if __name__ == "__main__":
    num = int(input())
    x = list(map(int, input().strip().split(' ')))
    minelement = min(x)
    minoutput = 0
    index = []
    for i in range(len(x)):
        if(x[i] == minelement):
            index.append(i)
    for i in range(len(index) - 1):
        tmp = index[i+1] - index[i]
        
        if(minoutput == 0):
            minoutput = tmp
        if(tmp < minoutput):
            minoutput = tmp
    print(minoutput)        
