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So i have experimented a bit with this exercise but im still not sure how to program it. If possible or if someone knows any algorithm for this exercise could you name it ?
As you know, on the ASM Olympiads teams wear t-shirts of different colors. All team members wear the same T-shirt. Each team chooses several different favorite colors from the set proposed by the organizers of the Olympiad. Each color offered by the organizers has a unique number from 1 to 100.
In many ways, the organizers of the Olympiad can assign each team a color from its set of favorite colors so that all teams have different colors of t-shirts. Two ways are considered different, if at least one team has a different color for T-shirts.
The first line of input contains the number of test cases T (1 ≤ T ≤ 10). Each test case contains the number N (1 ≤ N ≤ 10) in the first line - the total number of instructions. Each of the following N lines contains from 1 to 100 different numbers, separated by spaces, the color numbers of the T-shirts that the i-th team prefers.
For each test case output a single number - the number of possible cases modulo 1000000007 = 109 + 7.\
5 100 1
We want to find how many ways exist for each team to have different colors and the colors that they picked .
For example in test case 1 :
We have 2 teams. The 1st one wants the t-shirts with the number (or color) 3 and 5
and 2nd team wants the t-shirt with the number 8 and 100 .
Then we look if the 1st team picks number 3 and the second team picks the number 8 and they are different (since 3 != 8) then our result has found one way (result++)
Later we do the same if the 1st team picks number 3 and 2nd team number 100 and 3 != 100 then result++
Then pick for the 1st team the number 5 and so on.....
In the end the result ( which is the number of ways for each team to have different colors and the colors of their own preference ) is equal to 4