Larry is looking for a mate, but since his is such a busy man he is employing two of his friends to help him.

There are candidate mates, each of which have two values: a beauty value and a personality value .

One of Larry's friends cares about both values, and will only consider a mate for larry if their beauty is at least and their personality is at least .

The other of his friends cares about the overall value, and will only consider a mate for Larry if their beauty value + their personality value is at least .

Larry doesn't know his friends' values of , , and though, so given triplets of integers , he wants you to detemine how many mates will be considered a candidate by both of his friends. Can you help him?

#### Input Specification

The first line will contain two integers and .

The next lines will contain two values

The next lines will contain three values , , and .

#### Output Specification

You are to output lines: the number of mates considered to be a candidate by both of his friends for each query.

#### Subtasks

##### Subtask 1 (2%)

##### Subtask 2 (20%)

,

##### Subtask 3 (21%)

,

##### Subtask 4 (57%)

No additional constraints.

#### Sample Input

```
5 4
35 100
70 70
45 15
80 40
20 95
20 50 120
10 10 100
60 60 80
0 100 100
```

#### Sample Output

```
2
4
1
1
```

## Comments