Problem Statement

An online judge has multiple judge servers that process submitted programs in parallel. Here, we focus on one of those servers.

This server's queue contains $N$ programs. Program $i$ takes $T_i-0.1$ seconds to execute.

At time $0$, the server is idle.

$N$ "execution commands" are sent to this server at times $s_1 < s_2 < \cdots < s_N$. When the server receives an execution command, if it is idle, it takes the program at the front of the queue and starts executing it. If it is executing a program, the program at the front of the queue is passed on to another server.

When program $i$ starts executing at time $t$, it finishes at time $t + T_i-0.1$ and the server returns to the idle state.

Find the number of programs executed on this server.

Input

$N$
$T_1\ T_2\ \ldots\ T_N$
$s_1\ s_2\ \ldots\ s_N$

Output

Output the number of programs executed on this server in 1 line.

Print a newline at the end.

Constraints

• $1 \le N \le 1000$
• $1 \le T_i \le 10^9$
• $1 \le s_1 < s_2 < \cdots < s_N \le 10^9$

Sample

3
2 3 1
1 4 6

2

5
1 2 3 4 1
1 2 4 5 8

4