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
def mp():return map(int,input().split())
def it():return int(input())

n=it()
l=list(mp())
m=min(l)
flag=0
ans=0
c=0
k=float('inf')
for i in range(len(l)):
	if l[i]==m:
		c+=1
		flag=1
		if ans>0:
			k=min(k,ans)
			ans=0
	elif flag==1:
		# c=0
		ans+=1
		if c<2:
			c=0
		else:
			pass
if c<2:
	print(k+1)
else:
	print(1)
