Convert little imperative code to functional coding style

[bioinfornatics]

Dear,
i try convert a code to functional coding style:

commented code is what i try to convert to functional


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import std.stdio;
import std.range;
import std.algorithm;
import std.conv         : to;
import std.typecons     : tuple;
import std.math         : sqrt, floor;
import std.array        : empty, array;


void main( ){
    immutable size_t limit = cast(size_t )
floor( sqrt( cast(double)1_000 ) );

    //~ foreach( m;  iota( 2, limit ) ){
        //~ foreach( n; iota( 1, m-1) ){
            //~ if( 2 * m * (m+n) == 1_000 ) writeln((m ^^ 2 - n ^^ 2) *
(2 * m * n) * (m ^^ 2 + n ^^ 2));
        //~ }
    //~ }

    auto r = iota(2, limit )
        .map!( m => tuple( m, iota( 1, m - 1)
                                .filter!( n => 2 * m * (m+n) == 1_000 )
                            )
            ).filter!( n => !n[1].empty );

    auto m = r.array[0][0];
    auto n = r.array[0][1];
    writeln( typeid( n ) );
    writeln(  n  );
    //~ writeln( (m ^^ 2 - n ^^ 2) * (2 * m * n) * (m ^^ 2 + n ^^ 2));
}

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I want to compute (m ^^ 2 - n ^^ 2) * (2 * m * n) * (m ^^ 2 + n ^^ 2)
when  n => 2 * m * (m+n) == 1_000

I do this in 2 step maybe that is possible in one.

I search to convert m and n to size_t type

thanks for your help