Tangram

Chen, your pretty sister, has been stuck on a tangram puzzle for an hour and came to you for help. The tangram is a puzzle rooted in China. The goal is to form a given shape using all seven pieces. Each piece can be placed anywhere, and rotated and flipped in any way, but pieces cannot overlap.

The seven pieces are:

• Two small right triangles (edge lengths $25\sqrt{2}$, $25\sqrt{2}$, and $50$)
• One medium right triangle (edge lengths $50$, $50$, and $50\sqrt{2}$)
• Two big right triangles (edge lengths $50\sqrt{2}$, $50\sqrt{2}$, and $100$)
• One square (side length $25\sqrt{2}$)
• One parallelogram (side lengths $25\sqrt{2}$ and $50$)

Given the shape of a polygon $P$, determine whether $P$ can be made by using all seven pieces. You may assume the following.

• Each edge of $P$ is parallel to the $x$-axis, the $y$-axis, the line $y = x$, or the line $y = -x$.
• $P$ is connected and has no hole. $P$ is a simple polygon, so its edges do not cross or touch each other.

The first line contains an integer $N$ ($3 \le N \le 30$), the number of vertices of $P$. Each of the next $N$ lines gives a vertex of $P$ in clockwise order. Each line contains four non-negative integers $a$, $b$, $c$, and $d$, separated by spaces. The vertex is at $(a + b\sqrt{2}, c + d\sqrt{2})$. No coordinate exceeds 1000.

Print "Yes" on a line if $P$ can be made with the seven pieces. Otherwise, print "No".