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).

Constraints

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

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.

Examples

Input

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

Output

COUNTER_CLOCKWISE CLOCKWISE

Input

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

Output

ONLINE_BACK ON_SEGMENT ONLINE_FRONT

inputFormat

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.

outputFormat

Output

For each query, print the above mentioned status.

Examples

Input

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

Output

COUNTER_CLOCKWISE CLOCKWISE

Input

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

Output

ONLINE_BACK ON_SEGMENT ONLINE_FRONT

样例

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

ONLINE_BACK
ON_SEGMENT
ONLINE_FRONT

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