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 sys

#f = open('input', 'r')
f = sys.stdin

n = int(f.readline())
s = list(map(int, f.readline().split()))

ans = 10000000000
min_val = 10000000000
min_last_pos = -1
for i in range(n):
  if min_val > s[i]:
    min_val = s[i]
    min_last_pos = i
    ans = 10000000000
  elif min_val == s[i]:
    if ans > i - min_last_pos:
      ans = i - min_last_pos
    min_last_pos = i

print(ans)
