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
from sys import stdin,stdout
#stdin.readline()
#stdout.write()
#raw_input()
#map(int,raw_input().split())
#map(int,stdin.readline().split())
n=int(stdin.readline())
a=map(int,stdin.readline().split())
t=min(a)
z=[]
for i in xrange(n):
    if a[i]==t:
        z.append(i)
q=n
l=len(z)
for i in xrange(l-1):
    q=min(q,z[i+1]-z[i])
print q