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
n = int(input())
numbers = input().split(" ")
minimum = None  # type: int
positions = []
for i in range(n):
    number = int(numbers[i])
    if minimum == number:
        positions.append(i)
    elif minimum is None or number < minimum:
        minimum = number
        positions = [i]
last_pos = positions[0]
min_distance = None
for i in range(1, len(positions)):
    distance = positions[i] - last_pos
    if min_distance is None or distance < min_distance:
        min_distance = distance
    last_pos = positions[i]
print(min_distance)
