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Let S be the set of all integer solution...

Let S be the set of all integer solutions, (x,y,z) of the system of equation
`x-2y+5z=0`
`-2x+4y + z=0`
`-7x+14 y + 9z =0`
such that `15 le x^2 + y^2 + z^2 le 150` . Then, the number of elements of the set S is equal to ________

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