Score : $1000$ points

Problem Statement

There is an infinitely large triangular grid, as shown below. Each point with integer coordinates contains a lamp.

Initially, only the lamp at $(X, 0)$ was on, and all other lamps were off. Then, Snuke performed the following operation zero or more times:

• Choose two integers $x$ and $y$. Toggle (on to off, off to on) the following three lamps: $(x, y), (x, y+1), (x+1, y)$.

After the operations, $N$ lamps $(x_1, y_1), \cdots, (x_N, y_N)$ are on, and all other lamps are off. Find $X$.

Constraints

• $1 \leq N \leq 10^5$
• $-10^{17} \leq x_i, y_i \leq 10^{17}$
• $(x_i, y_i)$ are pairwise distinct.
• The input is consistent with the statement, and you can uniquely determine $X$.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$:$

$x_N$ $y_N$

Output

Print $X$.

4
-2 1
-2 2
0 1
1 0

-1

The following picture shows one possible sequence of operations: