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Teams

Time limit 2 seconds
Memory limit 128 MiB

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 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 aregiven in the table below.

prb7768.gif

On the first day there are m = 2 projects. The required team sizes are k[0] = 1 and 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 m = 2 projects again, but this time the required team sizes are k[0] = 1 and 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.

Your 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. The sum of m across all queries will be equal to s (not given in the input, s200000). For each question, your program must return whether it is possible to form all the teams.

Input data

First line contains the number n (1n500000) of students. Each of the next n lines contains a pair of space-separated integers a[i] and b[i] (1a[i], b[i]n), where a[i] is the minimum team size for student i and b[i] is the maximum team size for student i. Next line contains the number of queries q (1q200000) to follow. Each of the next q lines consists of a query in the format m, k[0], k[1], ..., k[m−1]. m (1mn) 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. It is known that 1k[i]n. Note that the sum of all k[i] may exceed n.

Output data

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

Examples

Input example #1
4
2 4
1 2
2 3
2 3
2
2 1 3
2 1 1
Output example #1
1
0
Source 2015 IOI, Day 1