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
def main():
    n=input()
    l=map(long,raw_input().split())
    r=l*1
    r.sort()
    m=r[0]
    k=[]
    for i in xrange(n):
        if l[i]==m:
            k.append(i)
    p=[]
    for i in xrange(1,len(k)):
        p.append(k[i]-k[i-1])
    #print p,k
    print min(p[:])
            
main()