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 math
n = int(input())
X = input()
x = X.split()
arr = []
m = math.inf
for i in x:
	i = int(i)
	if i<m:
		m = i
for i in range(len(x)):
	if int(x[i]) == int(m):
		arr.append(i)		
temp = arr[1]-arr[0]		
for i in range(len(arr)-1):
	if (arr[i+1]-arr[i])<temp:
		
		temp = arr[i+1]-arr[i]	
print(temp)