Problem: For given n points in metric space, find the distance of the closest points.

Constraints

* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100

Input


n
x0 y0
x1 y1
:
xn-1 yn-1


The first integer n is the number of points.

In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.

Output

Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

2
0.0 0.0
1.0 0.0


Output

1.000000


Input

3
0.0 0.0
2.0 0.0
1.0 1.0


Output

1.41421356237

Solution (in PYTHON3):

Solution:
import sys
from operator import itemgetter
from itertools import permutations
from math import sqrt

def solve(a: list):
    length = len(a)
    if length <= 3:
        return min(sqrt((p1[0]-p2[0])**2+(p1[1]-p2[1])**2) for p1, p2 in permutations(a, 2))

    x_set_len = len(set(x for (x, _) in a))
    axis = 0 if x_set_len > length/2 else 1
    a.sort(key=itemgetter(axis))
    mid_index = length//2
    left, right = a[:mid_index], a[mid_index:]
    delta = min(solve(left), solve(right))
    median = a[mid_index][axis]
    m_a = []
    append = m_a.append
        
    for p in left[::-1]:
        if p[axis] < median-delta:
            break
        append(p)
    for p in right:
        if p[axis] > median+delta:
            break
        append(p)
    m_a.sort(key=itemgetter(not axis))

    for i, p1 in enumerate(m_a):
        ub = p1[not axis] + delta
        for j, p2 in enumerate(m_a[i+1:]):
            if p2[not axis] > ub:
                break
            dist = sqrt((p1[0]-p2[0])**2+(p1[1]-p2[1])**2)
            if dist < delta:
                delta = dist

    return delta

if __name__ == "__main__":
    N = int(input())
    a = [tuple(map(float, l.split())) for l in sys.stdin.readlines()]
    print("{:.10f}".format(solve(a)))