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Let A,B,C, and D be points in the plane with AB = AC = BC = BD = CD = 36 and such that A != D. Point K lies on segment AC such that AK = 2KC. Point M lies on segment AB, and point N lies on line AC, such that D, M, and N are collinear. Let lines CM and BN intersect at P. Then the maximum possible length of segment KP can be expressed in the form m+sqrt(n) for positive integers m and n. Compute 100m + n.