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/env python3
from sys import stdin, stdout

def rint():
    return map(int, stdin.readline().split())
n = int(input())
a = list(rint())
b = []
for i in range(n):
    b.append([a[i], i])
b.sort()

min_val = b[0][0]
c = []
for i in range(n):
    if b[i][0] == min_val:
        c.append(b[i][1])

min_dist = 10**100
for i in range(len(c)-1):
    i1 = c[i]
    i2 = c[i+1]
    dist = c[i+1] - c[i]
    if dist < min_dist:
        min_dist = dist

print(min_dist)
