Legendary.....?????

How many ordered triples x,y,z\color{#3D99F6}{x,y,z} satisfy

x2+y2+z2=343\color{#3D99F6}{x}^2+\color{#3D99F6}{y}^2+\color{#3D99F6}{z}^2 = 343

x,y,z\color{#3D99F6}{x,y,z } are positive integers.

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