The twelve months January, February, March, .........., November and December (in that order) of a year are respectively assigned the values 0,1,2,.....,10 and 11.

A given month corresponding to a specific year is defined as succinct when the remainder obtained by dividing a given year by 12 precisely corresponds to the value assigned to a month containing five Sundays. For example, 1990 when divided by 12 yields a remainder of 10; but November, 1990 did not contain five Sundays. Consequently November, 1990 was not a succinct month.

Considering all the succinct months occurring between 1945 A.D. and 2176 A.D. inclusively in accordance with the Gregorian calendar system, when does the 50^th succinct month occur? Determine the maximum number of years between two consecutive succinct months in the stated period.