Let ABC be a triangle with AB=80,BC=100,AC=60. Let D,E,F lie on BC,AC,AB such that CD=10,AE=45,BF=60. Let P be a point in the plane of triangle ABC. The minimum possible value of AP+BP+CP+DP+EP+FP can be expressed in the form x+y+z for integers x,y,z. Find x+y+z.Proposed by Yang Liu