Two sequences of length $N$, $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_N$, are given. Write a program to process the following queries:

• i j k: output the number of pairs $(p, q)$ such that $i \le p, q \le j$ and $A_p \times B_q \le k$.

Input

The first line gives the length $N$ of the sequences $(1 \le N \le 100{,}000)$.

The second line gives $A_1, A_2, \ldots, A_N$ $(1 \le A_i \le 100{,}000)$.

The third line gives $B_1, B_2, \ldots, B_N$ $(1 \le B_i \le 100{,}000)$.

The fourth line gives the number of queries $M$ $(1 \le M \le 100{,}000)$.

The next $M$ lines each give a query $i, j, k$ $(1 \le i \le j \le N, 1 \le k \le 100{,}000)$.

Output

For each query, output the answer on a single line.

Examples

Input 1

5
1 1 1 1 1
1 1 1 1 1
1
1 5 1

Output 1

25