During comparison-based sorting, you need a way to figure out an "order", i.e. which element goes before another element. The third argument does that for the case N=2, in comparing the relative order of 2 elements. This function just helps you figure out the order of x and y for any arbitrary x and y. Note that your comparator must follow some basic properties, else you won't get the expected results. Link to very helpful blog

1. (_) % X => [0, X-1]

2. (_) % 2 => [0, 1]

3. EVEN % 2 < ODD % 2

You can observe the third argument is sorting the array based on the above results. Since (even) % 2 < (odd) % 2, all the even elements will get pushed to left extremity of the array and vice versa for odd elements.

Now if you want to preserve the non-decreasing nature on the two counterparts (odd & even) you can modify the function as follows.

sort(all(a), [&](int x, int y) {
        if(x%2==y%2) {
            return x < y;
        }
        return x%2<y%2;  
    });