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
a = raw_input()
b = raw_input()

a = int(a[0])
b = b.split()

for i in range(len(b)):
	b[i] = int(b[i])

#print a 
#print b 

out = min(b)

temp = []

for i in range(len(b)):
	if(b[i] == out):
		temp.append(i)

temp2 = []

for i in range(1, len(temp)):
	temp2.append(temp[i] - temp[i-1])

out2 = min(temp2)

print out2






