Refer to the data below and answer the questions that follow

A group of six students picked up a number of iden cal candies from a bowl of candies kept in the class. It is known that the number of candies picked up by each student was no greater than 60 and no fewer than 40. Total number of candies picked up by the six students taken together was 286. No two students picked up equal number of candies.

Following points are known:
1. The numbers of candies picked up by exactly two students were even.
2. The numbers of candies picked up by exactly four students out of six were less than 50.
3. The numbers of candies picked up by exactly four students out of six were more than 44.
4. There are two sets of three students such that the numbers of candies with them form Arithme c Progressions with Common Difference 2 and 4 respectively. Exactly two students are common between these two sets of three students.

We define a set of the number of candies with the six students, when arranged in the ascending order i.e. T ≡ {S1, S2, S3, S4, S5, S6}, where S1, S2,..., S6 are the number of candies with the six students such that S1 < S2 < S3 < S4 < S5 < S6.