Score : $1200$ points

Problem Statement

Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.

On a number line, there are $N$ copies of Takahashi, numbered $1$ through $N$. The $i$-th copy is located at position $X_i$ and starts walking with velocity $V_i$ in the positive direction at time $0$.

Kenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else.

Kenus can select some of the copies of Takahashi at time $0$, and transform them into copies of Aoki, another Ninja. The walking velocity of a copy does not change when it transforms. From then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki.

Among the $2^N$ ways to transform some copies of Takahashi into copies of Aoki at time $0$, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time? Find the count modulo $10^9+7$.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq X_i,V_i \leq 10^9(1 \leq i \leq N)$
• $X_i$ and $V_i$ are integers.
• All $X_i$ are distinct.
• All $V_i$ are distinct.

Input

The input is given from Standard Input in the following format:

$N$

$X_1$ $V_1$

:

$X_N$ $V_N$

Output

Print the number of the ways that cause all the copies of Takahashi to turn into copies of Aoki after a sufficiently long time, modulo $10^9+7$.

3
2 5
6 1
3 7

6

All copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: $(2)$, $(3)$, $(1,2)$, $(1,3)$, $(2,3)$ and $(1,2,3)$.

4
3 7
2 9
8 16
10 8

9