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
N=input()
A=raw_input().split(" ")
MIN=10000000000
for x in A:
	n=int(x)
	if n<MIN:
		MIN=n
last=0
for x in A:
	n=int(x)
	if n==MIN:
		break
	last+=1
ANS=10000000000
for x in range(last+1,N):
	n=int(A[x])
	if n==MIN:
		ANS=min(ANS,x-last)
		last=x
print ANS