Paired Up

문제

There are a total of $NN$ ($1\le N\le {10}^{5}1\backslash le\; N\backslash le\; 10^5$) cows on the number line. The location of the $ii$-th cow is given by $x_{i}x\_i$ ($0\le x_i\le {10}^{9}0\; \backslash leq\; x\_i\; \backslash leq\; 10^9$), and the weight of the $ii$-th cow is given by $y_{i}y\_i$ ($1\le y_i\le {10}^{4}1\; \backslash leq\; y\_i\; \backslash leq\; 10^4$).

At Farmer John's signal, some of the cows will form pairs such that

• Every pair consists of two distinct cows $aa$ and $bb$ whose locations are within $KK$ of each other ($1\le K\le {10}^{9}1\backslash le\; K\backslash le\; 10^9$); that is, $\mathrm{\mid }{x}_a-x_b\mathrm{\mid }\le K|x\_a-x\_b|\backslash le\; K$.
• Every cow is either part of a single pair or not part of a pair.
• The pairing is maximal; that is, no two unpaired cows can form a pair.

It's up to you to determine the range of possible sums of weights of the unpaired cows. Specifically,

• If $T=1T=1$, compute the minimum possible sum of weights of the unpaired cows.
• If $T=2T=2$, compute the maximum possible sum of weights of the unpaired cows.

입력

The first line of input contains $TT$, $NN$, and $KK$.

In each of the following $NN$ lines, the $ii$-th contains $x_{i}x\_i$ and $y_{i}y\_i$. It is guaranteed that .

출력

Please print out the minimum or maximum possible sum of weights of the unpaired cows.

2 5 2
1 2
3 2
4 2
5 1
7 2

6

1 5 2
1 2
3 2
4 2
5 1
7 2

2

2 15 7
3 693
10 196
12 182
14 22
15 587
31 773
38 458
39 58
40 583
41 992
84 565
86 897
92 197
96 146
99 785

2470