Reflection

For given three points p1, p2, p, find the reflection point x of p onto p1p2.

Constraints

• 1 ≤ q ≤ 1000
• -10000 ≤ xi, yi ≤ 10000
• p1 and p2 are not identical.

Input

xp1 yp1 xp2 yp2 q xp0 yp0 xp1 yp1 ... xpq−1 ypq−1

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

Output

For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.

Examples

Input

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

Output

-1.0000000000 -1.0000000000 0.0000000000 -1.0000000000 1.0000000000 -1.0000000000

Input

0 0 3 4 3 2 5 1 4 0 3

Output

4.2400000000 3.3200000000 3.5600000000 2.0800000000 2.8800000000 0.8400000000

inputFormat

Input

xp1 yp1 xp2 yp2 q xp0 yp0 xp1 yp1 ... xpq−1 ypq−1

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

outputFormat

Output

For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.

Examples

Input

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

Output

-1.0000000000 -1.0000000000 0.0000000000 -1.0000000000 1.0000000000 -1.0000000000

Input

0 0 3 4 3 2 5 1 4 0 3

Output

4.2400000000 3.3200000000 3.5600000000 2.0800000000 2.8800000000 0.8400000000

样例

0 0 3 4
3
2 5
1 4
0 3

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

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