The number of solutions (x, y, z) to the system of equations
\[x+2y+4z=9\]
\[4yz+2xz+xy=13\]
\[xyz=3\]
such that at least two of x, y, z are integers is
\[Note-\:\:Its\:\:an\:\:old\:\:KVPY\:\:question\]

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