Bobo has drawn three line segments $s_1$, $s_2$, and $s_3$ on a plane. The left endpoint of segment $s_i$ is $(a_i, y_i)$ and the right endpoint is $(b_i, y_i)$. Determine whether it is possible to find three points $p_1$, $p_2$, and $p_3$ such that:

• $p_i$ lies on segment $s_i$;
• $p_1$, $p_2$, and $p_3$ are collinear.

Input

The input contains multiple test cases. Process until the end of the file.

Each test case consists of three lines. The first line contains three integers $a_1, b_1, y_1$. The second line contains three integers $a_2, b_2, y_2$. The third line contains three integers $a_3, b_3, y_3$.

• $0 \leq a_i < b_i \leq 10^9$
• $0 \leq y_1 < y_2 < y_3 \leq 10^9$
• The number of test cases does not exceed $10^4$.

Output

For each test case, output Yes if three such collinear points exist, otherwise output No.

Examples

Input 1

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

Output 1

Yes
Yes
No