Order of Digits

You will be given a list $L$ consisting of $N$ non-negative integers in a decimal number system. We all know that, in the decimal number system, there are 10 digits $(0,1,2,3,4,5,6,7,8,9)$. Their order is defined as $(0 < 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9)$.

In this problem, you will be given some queries. In each query, you will be given a modified order of the 10 digits as a list $P$ and an integer, $X$. Here, $P$ denotes the modified order of digits as $P[0] < P[1] < P[2] < P[3] < P[4] < P[5] < P[6] < P[7] < P[8] < P[9]$. The answer to the query is the number of integers that are less than the given integer $X$ in list $L$ (applying the modified digit order described by $P$). The order of digit $0$ will not be modified.

Input

First line of the input contains a single integer $N$$(1 \leq N \leq 10^5)$. The next line will contain $N$ space-separated integers $L_{0}, L_{1}, … , L_{N-1}$ which are the elements of the list $L$ and $0 \leq L_{i} \leq 10^{18}$.

After that, there will be an integer $Q(1 \leq Q \leq 10^5)$ denoting the number of queries. Each of the queries will contain $11$ space-separated integers. The first $10$ integers will denote the list, $P$. The $11^\text{th}$integer will denote the value of $X$ $(0 \leq X \leq 10^{18})$. It is guaranteed that $P[0] = 0$ for each of the queries.

Output

For each test case, print the number of integers that are less than the given integer $X$ in list $L$ applying modified digit priority. Print the answer in a new line.

Sample

Input	Output
3 10 20 30 1 0 9 8 7 6 5 4 3 2 1 10	2
Given, List $L = [10,20,30]$ Then, there were $Q = 1$ queries are asked. We can see that the query gives us a list $P = [0,9,8,7,6,5,4,3,2,1]$ and $X = 10$. From description of the problem, we know the relation given below. $P[0] < P[1] < P[2] < P[3] < P[4] < P[5] < P[6] < P[7] < P[8] < P[9]$ It yields the relation between digits $1, 2$ and $3$ as below: $3 < 2 < 1$ So, in the modified order of digits, $30$ and $20$ are smaller than $10$.