IOI '15 P3 - Teams (Standard I/O)

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Points: 35 (partial)
Time limit: 1.4s
Memory limit: 512M

Problem type

There is a class of N students, numbered 0 through N-1. Every day the teacher of the class has some projects for the students. Each project has to be completed by a team of students within the same day. The projects may have various difficulty. For each project, the teacher knows the exact size of a team that should work on it.

Different students may prefer different team sizes. More precisely, student i can only be assigned to a team of size between A[i] and B[i] inclusive. On each day, a student may be assigned to at most one team. Some students might not be assigned to any teams. Each team will work on a single project.

The teacher has already chosen the projects for each of the next Q days. For each of these days, determine whether it is possible to assign students to teams so that there is one team working on each project.


Suppose there are N=4 students and Q=2 days. The students' constraints on team sizes are given in the table below:


On the first day there are M=2 projects. The required team sizes are \mathrm K[0]=1 and \mathrm K[1]=3. These two teams can be formed by assigning student 0 to a team of size 1 and the remaining three students to a team of size 3.

On the second day there are projects M=2 again, but this time the required team sizes are \mathrm K[0]=1 and \mathrm K[1]=1. In this case it is not possible to form the teams, as there is only one student who can be in a team of size 1.

You are given the description of all students: N, A, and B, as well as a sequence of Q queries — one about each day. Each question consists of the number M of projects on that day and a sequence K of length M containing the required team sizes. For each question, your program must return whether it is possible to form all the teams.

Input Specification

Line 1 of input will contain a single integer N, representing the number of students.
Lines 2, \ldots, N + 1 will each contain a pair of space-separated integers \mathrm A[i] and \mathrm B[i], representing the length N arrays A and B, where \mathrm A[i] is the minimum team size for student i and \mathrm B[i] is the maximum team size for student i.
Line N + 2 will contain a single integer Q, representing the number of queries to follow.
Lines N + 3, \ldots, N + Q + 2 will each consists of a query in the format M, \mathrm K[0], \mathrm K[1], \ldots, \mathrm K[M - 1]. M represents the number of projects for this day and K is an array of length M containing the required team size for each of these projects.

Output Specification

For each query, output a separate line containing either 1 if it is possible to form all the required teams, or 0 otherwise.

Sample Input

2 4
1 2
2 3
2 3
2 1 3
2 1 1

Sample Output



Let us denote by S the sum of values of M.

subtask points N Q Additional Constraints
1 21 1 \le N \le 100 1 \le Q \le 100 none
2 13 1 \le N \le 100\,000 Q = 1 none
3 43 1 \le N \le 100\,000 1 \le Q \le 100\,000 S \le 100\,000
4 23 1 \le N \le 500\,000 1 \le Q \le 200\,000 S \le 200\,000