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 stdin
def solve(n,l):
	ocur = {}
	min__ = float('inf')
	for i in range(n):
		if ocur.get(l[i])!=None:
			ocur[l[i]].append(i)
		else:
			min__ = min(min__,l[i])
			ocur[l[i]] = [i]
	min_arr = ocur.get(min__)
	ans = float('inf')
	for j in range(len(min_arr)-1):
		ans = min(ans,min_arr[j+1]-min_arr[j])
	return ans


def main():
	n = int(stdin.readline().strip())
	l = [int(x) for x in stdin.readline().split()]
	print(solve (n,l))

main()
				 	  	  		  	  	 					  		 	