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
from collections import defaultdict
n = int(stdin.readline(),10)
mini, pos, c, min_abs = 1000000001, defaultdict(list), 1, 1000000001
for j in stdin.readline().strip().split():
    j = int(j,10)
    pos[j].append(c)
    mini = min(j, mini)
    c+=1
for i in xrange(len(pos[mini])-1):
    sub = pos[mini][i + 1] - pos[mini][i]
    min_abs = min(sub, min_abs)
stdout.write(str(min_abs))