When I compute the following expression to find integer solutions of the equation `(x^2 + y^2 + z^2 == 14^2)`

    Solve[x^2 + y^2 + z^2 == 14^2 && x > 0 && y > 0 && z > 0, {x, y, z}, Integers]

Mathematica returns

    {{x -> 4, y -> 6, z -> 12}, {x -> 4, y -> 12, z -> 6}, {x -> 6, y -> 4, z -> 12}, 
     {x -> 6, y -> 12, z -> 4}, {x -> 12, y -> 4, z -> 6}, {x -> 12, y -> 6, z -> 4}}

which are permutations of the only solution: x=4, y=6, z=12.

How can I remove other "solutions" by somehow merging the permutations? For me, x, y, and z are equivalent.

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I don't want to do the following:

    First[Solve[x^2 + y^2 + z^2 == 14^2 && x > 0 && y > 0 && z > 0, {x, y, z}, Integers]]

Because I will also solve:

    Solve[x^2 + y^2 + z^2 == 14^3 && x > 0 && y > 0 && z > 0, {x, y, z}, Integers]

which has more than one solution.