<p>Given an integer <code>n</code>, return <em>a list of all <strong>simplified</strong> fractions between </em><code>0</code><em> and </em><code>1</code><em> (exclusive) such that the denominator is less-than-or-equal-to </em><code>n</code>. You can return the answer in <strong>any order</strong>.</p>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> [&quot;1/2&quot;]
<strong>Explanation:</strong> &quot;1/2&quot; is the only unique fraction with a denominator less-than-or-equal-to 2.
</pre>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> [&quot;1/2&quot;,&quot;1/3&quot;,&quot;2/3&quot;]
</pre>

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

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> [&quot;1/2&quot;,&quot;1/3&quot;,&quot;1/4&quot;,&quot;2/3&quot;,&quot;3/4&quot;]
<strong>Explanation:</strong> &quot;2/4&quot; is not a simplified fraction because it can be simplified to &quot;1/2&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
</ul>

class Solution {
public:

    string modified ( int a, int b )
    {
        int gcd = 1;

        for ( int i = 2; i <= a; ++i )
        {
            if ( a % i == 0 && b % i == 0 )
                gcd = i;

            if ( gcd > i )
                i = gcd;
        }

        return to_string(a/gcd) + '/' + to_string(b/gcd);
    }

    vector<string> simplifiedFractions(int n) {

        vector<string> a;

        for ( int i = 1; i < n; ++i )
        {
            for ( int j = i+1; j <= n; ++j )
            {
                string s = modified(i,j);

                int k = 0;

                for ( ; k < a.size(); ++k )
                {
                    if ( a[k] == s )
                        break;
                }

                if ( k >= a.size() )
                    a.push_back(s);
            }          
        }

        return a;
        
    }
};
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