Naruto (young) performing his Shadow Clone Jutsu.

Naruto's signature jutsu is the shadow clone jutsu. He can create over 200000 clones of himself!

On a line, Naruto has created ~N~ copies of himself. He has numbered each of his clones from ~1~ to ~N~. His ~i^{th}~ clone, located at position ~P_i~, will begin walking with a velocity of ~V_i~ towards the positive direction at time ~0~.

As Sasuke and Naruto are such great rivals, Sasuke has mastered a... new type of jutsu. At time ~0~, he can choose a number of shadow clones, and that clone will turn into a clone of Sasuke! When the clone turns into Sasuke, the velocity and position of the clone will not change, and it will continue walking towards the positive direction. Furthermore, once a Sasuke clone touches another Naruto clone, the Naruto clone will become a Sasuke clone!

There are many clones Sasuke could choose at time ~0~ to transform all of the Naruto clones to Sasuke clones. How many ways will all of Naruto's clones turn into Sasuke clones after an infinitely large amount of time?

Constraints

• ~1 \le N \le 200000~
• ~1 \le P_i, V_i \le 10^9~, such that ~1 \le i \le N~
• All values of ~P_i~ will be distinct, and so will ~V_i~.

Input Specification

The first line of input will contain an integer ~N~.

The next ~N~ lines of input will contain 2 space separated integers, ~P_i~ and ~V_i~.

Output Specification

You are to output a single integer, the number of ways at time ~0~ to change a number of Naruto clones to Sasuke clones, modulo ~10^9 + 7~.

Sample Input 1

3
2 5
6 1
3 7

Sample Output 1

6

Sample Explanation

After an infinitely large amount of time, the ways Sasuke could choose clones at time ~0~ are:

~(2)~, ~(3)~, ~(1, 2)~, ~(1, 3)~, ~(2, 3)~, ~(1, 2, 3)~.