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

<image>

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.

Example

Input

4
-2 1
-2 2
0 1
1 0

Output

-1

见题面

见题面