Contest Duration: - (local time) (100 minutes) Back to Home
B - Longest Segment /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

この中から 2 個の点を選ぶとき、それらを結ぶ線分の長さの最大値を求めてください。

### 制約

• 2 \leq N \leq 100
• -1000 \leq x_i,y_i \leq 1000
• (x_i,y_i) \neq (x_j,y_j)\ (i \neq j)
• 入力はすべて整数

### 入力

N
x_1 y_1
x_2 y_2
\hspace{0.4cm} \vdots
x_N y_N


### 出力

2 点を結ぶ線分の長さの最大値を出力せよ。

### 入力例 1

3
0 0
0 1
1 1


### 出力例 1

1.4142135624


1 個目の点と 3 個目の点を選んだときそれらを結ぶ線分の長さは \sqrt 2 = 1.41421356237\dots となり、これが最大です。

### 入力例 2

5
315 271
-2 -621
-205 -511
-952 482
165 463


### 出力例 2

1455.7159750446


Score : 200 points

### Problem Statement

There are N points in a two-dimensional plane. The coordinates of the i-th point are (x_i,y_i).

Find the maximum length of a segment connecting two of these points.

### Constraints

• 2 \leq N \leq 100
• -1000 \leq x_i,y_i \leq 1000
• (x_i,y_i) \neq (x_j,y_j)\ (i \neq j)
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
\hspace{0.4cm} \vdots
x_N y_N


### Output

Print the maximum length of a segment connecting two of the points.

Your answer will be considered correct when the absolute or relative error from the judge's answer is at most 10^{-6}.

### Sample Input 1

3
0 0
0 1
1 1


### Sample Output 1

1.4142135624


For the 1-st and 3-rd points, the length of the segment connecting them is \sqrt 2 = 1.41421356237\dots, which is the maximum length.

### Sample Input 2

5
315 271
-2 -621
-205 -511
-952 482
165 463


### Sample Output 2

1455.7159750446