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
what=raw_input()
l=raw_input()
l=l.split(' ')
l=[int(x) for x in l]
min_num=min(l)
ind=[]
for i ,val in enumerate(l):
	if val==min_num:
		ind.append(i)
min_dist=ind[1]-ind[0]
for i in range(1,len(ind)-1):
	if ind[i+1]-ind[i]<min_dist:
		min_dist=ind[i+1]-ind[i]
print min_dist
		
