# Points/Vectors - Counter-Clockwise

Time Limit : 1 sec, Memory Limit : 131072 KB
Japanese version is here

# Counter-Clockwise

For given three points p0, p1, p2, print

```COUNTER_CLOCKWISE
```

if p0, p1, p2 make a counterclockwise turn (1),

```CLOCKWISE
```

if p0, p1, p2 make a clockwise turn (2),

```ONLINE_BACK
```

if p2 is on a line p2, p0, p1 in this order (3),

```ONLINE_FRONT
```

if p2 is on a line p0, p1, p2 in this order (4),

```ON_SEGMENT
```

if p2 is on a segment p0p1 (5).

## Input

```xp0 yp0 xp1 yp1
q
xp20 yp20
xp21 yp21
...
xp2q-1 yp2q-1
```

In the first line, integer coordinates of p0 and p1 are given. Then, q queries are given for integer coordinates of p2.

## Output

For each query, print the above mentioned status.

## Constraints

• 1 ≤ q ≤ 1000
• -10000 ≤ xi, yi ≤ 10000
• p0 and p1 are not identical.

## Sample Input 1

```0 0 2 0
2
-1 1
-1 -1
```

## Sample Output 1

```COUNTER_CLOCKWISE
CLOCKWISE
```

## Sample Input 2

```0 0 2 0
3
-1 0
0 0
3 0
```

## Sample Output 2

```ONLINE_BACK
ON_SEGMENT
ONLINE_FRONT
```