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=input()
l=[int(i) for i in raw_input().split()]
a=min(l)
s=[]
for i in range(n):
    if l[i]==a:
        s.append(i+1)
s.sort()
d=[]
for i in range(len(s)-1):
    d.append(math.fabs(s[i+1]-s[i]))
print int(min(d))
