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 combinations, takewhile
from math import sqrt

def solve(a: list, sorted_axis: int = -1):
    length = len(a)
    if length <= 3:
        return sqrt(min((x1-x2)**2+(y1-y2)**2 for (x1, y1), (x2, y2) in combinations(a, 2)))

    x_set_len = len(set(x for x, _ in a))
    axis1 = 0 if x_set_len > length/2 else 1

    if sorted_axis != axis1:
        a.sort(key=itemgetter(axis1))

    mid_index = length//2
    left, right = a[:mid_index], a[mid_index:]
    delta = min(solve(left, axis1), solve(right, axis1))

    axis2 = not axis1
    median = a[mid_index][axis1]
    mid_a = sorted([p for _iter in (
        (takewhile(lambda p: median-delta < p[axis1], left[::-1])),
        (takewhile(lambda p: p[axis1] < median+delta, right))
    ) for p in _iter], key=itemgetter(axis2))

    for i, (x1, y1) in enumerate(mid_a):
        ub = (x1 if axis1 else y1) + delta
        for x2, y2 in takewhile(lambda p: p[axis2] < ub, mid_a[i+1:]):
            delta = min(delta, sqrt((x1-x2)**2+(y1-y2)**2))

    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)))