<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 {
private:
    int distance(int x1 , int y1 , int x2 , int y2)
    {
        int num= pow((x1-x2),2) + pow((y1-y2),2);
        return (num);
    }

public:
    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        int d1=distance(p1[0],p1[1],p4[0],p4[1]);
        int d2=distance(p1[0],p1[1],p3[0],p3[1]);
        int d3=distance(p1[0],p1[1],p2[0],p2[1]);
        int d4=distance(p2[0],p2[1],p4[0],p4[1]);
        int d5=distance(p4[0],p4[1],p3[0],p3[1]);
        int d6=distance(p2[0],p2[1],p3[0],p3[1]);
        
        vector<int> dist={d1,d2,d3,d4,d5,d6};
        sort(dist.begin(),dist.end());

        if(dist[0]>0 and dist[0]==dist[1] and dist[1]==dist[2] and dist[2]==dist[3] and dist[4]==dist[5]) return true;
        return false;
    }
};
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