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 pprint import pprint as pp
def GI(): return int(input())
def GIS(): return map(int, input().split())

def main():
  input()
  a = list(GIS())
  m = min(a)

  last_min_index = None
  min_dist = len(a) + 1
  for i, d in enumerate(a):
    if d != m:
      continue
    if last_min_index is not None:
      min_dist = min([i - last_min_index, min_dist])
    last_min_index = i
  print(min_dist)

main()
