# A Conference commenced on a given day precisely at M*X/ 143 minutes past P o'clock ( but before P+1 o'clock) and concluded at M*R(X) / 143 minutes past Q o'clock ( but before Q+1 o'clock) on the same day ; where 11 >=Q > P >=1 with the proviso that P and Q are whole numbers and M is a positive integer greater than 1.

#It was observed that the hour hand and the minute hand had exchanged places during the respective times of commencement and conclusion of the said conference.

# Determine the total number of distinct choices of the pentuplet (M,X,R(X),P,Q) satisfying conditions of the problem.

NOTE:

(i)Any two choices of the pentuplet are defined to be distinct if they differ in the magnitudes of at least one of the five parameters (viz. M,X.R(X),P and Q).

(ii)It may be noted that Q is always greater than P. For example, (P=2,Q=3) may correspond to valid values for P and Q, but (P=3,Q=2) is not feasible.