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
import sys

ls = []
length = int(sys.stdin.readline())
y = 0
for l in sys.stdin.readline().split(' '):
	ls.append(int(l))

#find minimum	
mini = sorted(ls)[0]
count = 0
currentNearest = 1000000
x = -1
isFound = False

#find first minimum
while x < length:
	while not isFound:
		x += 1
		if x < length:
			isFound = (ls[x] == mini)
		else:
			break
	isFound = False
	#count to next minimum
	while not isFound:
		x += 1
		count += 1
		if x < length:
			isFound = (ls[x] == mini)
		else:
			break
	if count < currentNearest and x < length:
		currentNearest = count
	count = 0

print currentNearest
