[HackerEarth] You are now studying in IIN and have to follow the curriculum. Here is how the curriculum is structured. - P18648

题目描述

You are now studying in IIN and have to follow the curriculum. Here is how the curriculum is structured.
There are a total of n faculties in this institute. The i^th faculty has mi different courses under his mentor-ship. Every course under a particular faculty might have some topics in common. Hence each course, under each faculty, have been given "Conceptual points", which indicate the level of toughness of that course. To qualify a course x, taught under faculty i, you first have to qualify all the courses y, taught under same faculty, such that the Conceptual Points of all y's is less than Conceptual points of x.
As per the rule, you have to complete every course that university offers, one at a time. Also, at any moment, when you select a new course, you will select only from those courses, which you can qualify at that time.
You can choose any course, under any faculty, in any semester, as long as above condition holds. A schedule is valid if all the courses taken as per the schedule do not violate the conditions mentioned above.
Note that all the courses are distinct and any 2 courses under different faculties have no dependency whatsoever.
Find total number of possible valid schedules. As answer can be large, output it modulo 10^9 + 7.
Input:
The first line of input will contain an integer n, the number of faculties. Next n lines each will first contain a letter mi, the number of courses under faculty i. The mi space separated integers will follow in the same line, where j^th integer xj will indicate the Conceptual Level of j^th course under i^th faculty.
Output:
Output the required answer modulo 10^9 + 7.
Constraints:
1 ≤ Total number of university courses ≤ 10^5
1 ≤ n ≤ 10^5
1 ≤ m ≤ 10^5
1 ≤ xj ≤ 10^5 for all i's
SAMPLE INPUT
2
2 1 2
2 1 2
SAMPLE OUTPUT
6
Explanation
Lets name the courses of first faculty as x and y. Lets name the courses of second faculty as z and w.
The possible schedules are (x,y,z,w), (x,z,y,w), (x,z,w,y), (z,x,w,y), (z,x,y,w) and (z,w,x,y). Hence the answer is 6.
输入格式

见题面
输出格式

见题面
样例输入

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样例输出

226800
时间限制	2000 ms
内存限制	256 MB
难度	普及
提交数	0
通过数	0
通过率	0.0%
P18648 [HackerEarth] You are now studying in IIN and have to follow the curriculum. Here is how the curriculum is structured.

题目描述

输入格式

输出格式

样例输入

样例输出
