Pac-Man

Task

Alessandro is coding his new 3D version of Pac-Man. The game board is described by a three-dimensional grid, some cells are blocked and the others are free. Pac-Man and the ghosts can move to any free cell sharing a face with the current cell.

Alessandro instructed ghosts to move in a very simple way. If a ghost wants to move from cell $A$ to cell $B$, it will repeat the following procedure until it reaches its destination or fails:

• If the ghost can decrease the distance along the $x$ axis (i.e. $|A_x - B_x|$) it will do so by moving one cell along the $x$ axis;
• otherwise if it can decrease the distance along the $y$ axis (i.e. $|A_y - B_y|$) it will do so by moving one cell along the $y$ axis;
• otherwise if it can decrease the distance along the $z$ axis (i.e. $|A_z - B_z|$) it will do so by moving one cell along the $z$ axis;
• otherwise it fails.

Alessandro has three arrays $X_i$, $Y_i$ and $Z_i$ indexed from $0$ to $N-1$ that describe the coordinates of the free cells.
He is wondering whether the strategy above is smart enough to control the ghosts.

Help him by writing a program that determines whether for every pair of cells $A$ and $B$ a ghost will succeed in reaching cell $B$ starting from cell $A$!

Input data

The input file consists of:

• a line containing integer $N$.
• a line containing the $N$ integers $X_{0}, \, \ldots, \, X_{N-1}$.
• a line containing the $N$ integers $Y_{0}, \, \ldots, \, Y_{N-1}$.
• a line containing the $N$ integers $Z_{0}, \, \ldots, \, Z_{N-1}$.

Output data

The output file must contain a single line consisting of YES if ghosts will always succeed in reaching their destinations or NO otherwise.

Constraints and clarifications

• $1 \le N \le 100 \ 000$.
• $0 \le X_i, Y_i, Z_i < 100 \ 000$ for each $i=0 \ldots N-1$.

Example 1

stdin

4
0 0 1 1
0 1 1 2
0 0 0 0

stdout

YES

Explanation

In the first sample case, ghosts can always reach their destination.
For example, a ghost can move from cell $A = (0, 0, 0)$ to cell $B = (1, 2, 0)$ following path $(0, 0, 0) \rightarrow (0, 1, 0) \rightarrow (1, 1, 0) \rightarrow (1, 2, 0)$.

Example 2

stdin

8
0 1 2 2 2 1 0 0
0 0 0 1 1 1 1 0
0 0 0 0 1 1 1 1

stdout

NO

Explanation

In the second sample case, ghost can't move from cell $A = (1, 0, 0)$ to cell $B = (1, 1, 1)$.

Example 3

stdin

5
0 0 1 1 2
0 1 1 0 2
0 0 0 0 2

stdout

NO