A rotor has the following properties

$\backslash$table$[[$Mass$,$Magnitude,Radius,Angle,$\backslash$table$[[$Axial distance$],[$from $1^{st}$ mass$]]],[1,9$ kg$,100$ mm$,0,],[2,7$ kg$,120$ mm$,60$ deg,$160$ mm$],[3,8$ kg$,140$ mm$,-135$ deg,$320$ mm$],[4,6$ kg$,120$ mm$,270$ deg,$560$ mm$]]$

If the shaft is balanced by two counter masses located at $100$ mm radii and revolving in planes midway of planes $1$ and $2$ and midway of $3$ and $4,$ determine the magnitude of the masses and their respective angular position for the reduced wear and tear of the shaft. $($Analytical method$)$