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
#!/usr/bin/python

def get_numbers():
  raw_input() # Remove first number
  return [int(x) for x in raw_input().split()]

def get_indices(nums, minimum):
  return [i for i in xrange(len(nums)) if nums[i] == minimum]

def get_minimum_distance(indices):
  minimum = indices[1] - indices[0]
  for i in xrange(1, len(indices)):
    minimum = min(minimum, indices[i] - indices[i-1])
  return minimum

def main():
  nums = get_numbers()
  minimum = min(nums)
  indices = get_indices(nums, minimum)
  print get_minimum_distance(indices)

if __name__ == '__main__':
  main()

