Gildong is experimenting with an interesting machine Graph Traveler. In Graph Traveler, there is a directed graph consisting of n vertices numbered from 1 to n. The i-th vertex has m_i outgoing edges that are labeled as e_i[0], e_i[1], …, e_i[m_i-1], each representing the destination vertex of the edge. The graph can have multiple edges and self-loops. The i-th vertex also has an integer k_i written on itself.

A travel on this graph works as follows. 

  1. Gildong chooses a vertex to start from, and an integer to start with. Set the variable c to this integer. 
  2. After arriving at the vertex i, or when Gildong begins the travel at some vertex i, add k_i to c. 
  3. The next vertex is e_i[x] where x is an integer 0 ≤ x ≤ m_i-1 satisfying x ≡ c \pmod {m_i}. Go to the next vertex and go back to step 2. 



It's obvious that a travel never ends, since the 2nd and the 3rd step will be repeated endlessly.

For example, assume that Gildong starts at vertex 1 with c = 5, and m_1 = 2, e_1[0] = 1, e_1[1] = 2, k_1 = -3. Right after he starts at vertex 1, c becomes 2. Since the only integer x (0 ≤ x ≤ 1) where x ≡ c \pmod {m_i} is 0, Gildong goes to vertex e_1[0] = 1. After arriving at vertex 1 again, c becomes -1. The only integer x satisfying the conditions is 1, so he goes to vertex e_1[1] = 2, and so on.

Since Gildong is quite inquisitive, he's going to ask you q queries. He wants to know how many distinct vertices will be visited infinitely many times, if he starts the travel from a certain vertex with a certain value of c. Note that you should not count the vertices that will be visited only finite times.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 1000), the number of vertices in the graph.

The second line contains n integers. The i-th integer is k_i (-10^9 ≤ k_i ≤ 10^9), the integer written on the i-th vertex.

Next 2 ⋅ n lines describe the edges of each vertex. The (2 ⋅ i + 1)-st line contains an integer m_i (1 ≤ m_i ≤ 10), the number of outgoing edges of the i-th vertex. The (2 ⋅ i + 2)-nd line contains m_i integers e_i[0], e_i[1], …, e_i[m_i-1], each having an integer value between 1 and n, inclusive.

Next line contains an integer q (1 ≤ q ≤ 10^5), the number of queries Gildong wants to ask.

Next q lines contains two integers x and y (1 ≤ x ≤ n, -10^9 ≤ y ≤ 10^9) each, which mean that the start vertex is x and the starting value of c is y.

Output

For each query, print the number of distinct vertices that will be visited infinitely many times, if Gildong starts at vertex x with starting integer y.

Examples

Input


4
0 0 0 0
2
2 3
1
2
3
2 4 1
4
3 1 2 1
6
1 0
2 0
3 -1
4 -2
1 1
1 5


Output


1
1
2
1
3
2


Input


4
4 -5 -3 -1
2
2 3
1
2
3
2 4 1
4
3 1 2 1
6
1 0
2 0
3 -1
4 -2
1 1
1 5


Output


1
1
1
3
1
1

Note

The first example can be shown like the following image:

<image>

Three integers are marked on i-th vertex: i, k_i, and m_i respectively. The outgoing edges are labeled with an integer representing the edge number of i-th vertex.

The travel for each query works as follows. It is described as a sequence of phrases, each in the format "vertex (c after k_i added)".

  * 1(0) → 2(0) → 2(0) → … 
  * 2(0) → 2(0) → … 
  * 3(-1) → 1(-1) → 3(-1) → … 
  * 4(-2) → 2(-2) → 2(-2) → … 
  * 1(1) → 3(1) → 4(1) → 1(1) → … 
  * 1(5) → 3(5) → 1(5) → … 



The second example is same as the first example, except that the vertices have non-zero values. Therefore the answers to the queries also differ from the first example.

<image>

The queries for the second example works as follows:

  * 1(4) → 2(-1) → 2(-6) → … 
  * 2(-5) → 2(-10) → … 
  * 3(-4) → 1(0) → 2(-5) → 2(-10) → … 
  * 4(-3) → 1(1) → 3(-2) → 4(-3) → … 
  * 1(5) → 3(2) → 1(6) → 2(1) → 2(-4) → … 
  * 1(9) → 3(6) → 2(1) → 2(-4) → …

Difficulty: HARD
Tags: Graph algorithms

Graph traversal

Implementation

Complete search

Number theory

Dynamic programming

Mathematics

Data structures
Skill types: Dynamic programming

Data structures

Complete search

Starter code:

Solutions:
import io, sys
input = lambda f=io.StringIO(sys.stdin.buffer.read().decode()).readline: f().rstrip()
LCM = 2520
n = int(input())
k = list(map(int, input().split()))
(m, e) = ([0] * n, [None] * n)
for i in range(n):
	m[i] = int(input())
	e[i] = list(map(int, input().split()))
nxt = []
for i in range(n):
	for j in range(LCM):
		x = (j + k[i]) % LCM
		y = e[i][x % m[i]] - 1
		nxt.append(y * LCM + x)
loop = [None] * (n * LCM)
for i in range(n * LCM):
	if loop[i]:
		continue
	loop[i] = set()
	(cur, rec) = (nxt[i], [i])
	while True:
		if loop[cur] is not None:
			break
		loop[cur] = loop[i]
		rec.append(cur)
		cur = nxt[cur]
	if loop[cur]:
		for u in rec:
			loop[u] = loop[cur]
	else:
		while rec[-1] != cur:
			loop[i].add(rec.pop() // LCM)
		loop[i].add(cur // LCM)
out = []
for _ in range(int(input())):
	(x, y) = map(int, input().split())
	out.append(len(loop[(x - 1) * LCM + y % LCM]))
print(*out, sep='\n')


import sys
from sys import stdin

def solve(v, c):
	if d[v][c] != None:
		return d[v][c]
	vnum = 0
	visits = set()
	while True:
		if c * n + v in visits:
			last = d[v][c]
			vs = set()
			for u in visits:
				if d[u % n][u // n] <= last:
					vs.add(u % n)
			nans = len(vs)
			for u in visits:
				d[u % n][u // n] = nans
			return nans
		elif d[v][c] != None and d[v][c] > 0:
			nans = d[v][c]
			for u in visits:
				d[u % n][u // n] = nans
			return nans
		visits.add(c * n + v)
		d[v][c] = vnum
		vnum -= 1
		c = (c + k[v]) % mod
		v = lis[v][c % len(lis[v])]
n = int(stdin.readline())
mod = 2520
d = [[None] * mod for i in range(n)]
k = list(map(int, stdin.readline().split()))
lis = []
for i in range(n):
	m = int(stdin.readline())
	lis.append(list(map(int, stdin.readline().split())))
	for j in range(m):
		lis[i][j] -= 1
q = int(stdin.readline())
ANS = []
for loop in range(q):
	(x, y) = map(int, stdin.readline().split())
	x -= 1
	ANS.append(solve(x, y % mod))
print('\n'.join(map(str, ANS)))