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
t=int(raw_input())
s=map(int,raw_input().strip().split(' '))
q=[]
a=[]
k=[]
for i in s:
    q.append(i)
s.sort()
l=s[0]
for i in range(0,t):
    if q[i]==l:
        a.append(i)
for i in range(1,len(a)):
    k.append(a[i]-a[i-1])
k.sort()
print k[0]
    
    
    

            



