<p>Given the coordinates of four points in 2D space <code>p1</code>, <code>p2</code>, <code>p3</code> and <code>p4</code>, return <code>true</code> <em>if the four points construct a square</em>.</p>

<p>The coordinate of a point <code>p<sub>i</sub></code> is represented as <code>[x<sub>i</sub>, y<sub>i</sub>]</code>. The input is <strong>not</strong> given in any order.</p>

<p>A <strong>valid square</strong> has four equal sides with positive length and four equal angles (90-degree angles).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
<strong>Output:</strong> false
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
<strong>Output:</strong> true
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>p1.length == p2.length == p3.length == p4.length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def validSquare(self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]) -> bool:
        a1=(p1[0]-p2[0])**2+(p1[1]-p2[1])**2
        a2=(p1[0]-p3[0])**2+(p1[1]-p3[1])**2
        a3=(p1[0]-p4[0])**2+(p1[1]-p4[1])**2
        a4=(p2[0]-p3[0])**2+(p2[1]-p3[1])**2
        a5=(p2[0]-p4[0])**2+(p2[1]-p4[1])**2
        a6=(p3[0]-p4[0])**2+(p3[1]-p4[1])**2
        l=[a1,a2,a3,a4,a5,a6]
        l.sort()
        if(l[0]>0 and l[0]==l[1]==l[2]==l[3] and l[4]==l[5] and l[4]>l[0]):
            return True
        else:
            return False

        
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