408633: GYM103241 H Position of Set

Teamscode has created a problem set for the constants to solve. A problem set consists of $$$N$$$ different problems with each problem having a difficulty $$$d$$$ (not necessarily distinct) and the difficulty is nondecreasing from $$$1$$$ to $$$N$$$. However, the day before the contest, Bossologist messed up and scrambled the problem set into a random order. The rest of the problem writing team is now angry at Bossologist, and would like to compute the number of possible original problem sets to make a case to HR.

The first line contains $$$N$$$ $$$(1 \leq N \leq 10^6)$$$.

The next $$$N$$$ lines contain a unique string $$$s$$$ and an integer $$$d$$$, where $$$s$$$ is the problem name, and $$$d$$$ is the problem difficulty. $$$(1 \leq d \leq 10^6)$$$ The sum of the lengths of all strings is guaranteed less than or equal to $$$10^7$$$.

Output the number of possible different original problem sets, given that a problem set has problem difficulties in a non-decreasing order, and considered distinct if a problem $$$p$$$ appears in a different spot for any $$$p$$$. Due to the large number of possible original problem sets, please output the answer mod $$$10^9 + 7$$$.

9
Average 1
Premins 9
Costs 2
Ordering 3
Books 3
ABCs 2
Mulitples 5
Teleport 2
P=NP 9

24

The answer is not 12... One possible original problem set is:

Average, Costs, ABCs, Teleport, Ordering, Books, Multiples, P=NP, and Premins in that order.

Another one is:

Average, ABCs, Costs, Teleport, Ordering, Books, Multiples, Premins, and P=NP.

Problem idea: Bossologist

Problem preparation: Bossologist

Occurances: Novice 8, Intermediate 5