Different Strokes

There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.

When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.

Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".

Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".

Constraints

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 B_1 : A_N B_N

Output

Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".

Examples

Input

3 10 10 20 20 30 30

Output

20

Input

3 20 10 20 20 20 30

Output

20

Input

6 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000

Output

-2999999997

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 B_1 : A_N B_N

outputFormat

Output

Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".

Examples

Input

3 10 10 20 20 30 30

Output

20

Input

3 20 10 20 20 20 30

Output

20

Input

6 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000

Output

-2999999997

样例

3
20 10
20 20
20 30

20