Problem

As the end of year $2015$ approaching, the downtown area has been lighted up to celebrate year’s end. At this year, Cat Snuke also enjoys making a light-up device for the downtown area.

The downtown can be regarded as a one-dimensional line of numbers. There are $N$ lights that have been installed on this number line. When the power of the $i_{th}$ light is on, it can illuminate an interval of \[l_i, r_i\] (inclusive).

Although Cat Snuke can switch on the $N$ lights independently as his wish, he wants to try different illumination combinations as many as possible. Then, if we had tried all the combinations of $2^N$ illumination combinations, we want to know how many different illumination combinations there are, of which each combination is a set of points that for each point in it can be illuminated by one or more lights.

When we tried all the $2^N$ illumination combination, please answer the number of the different illumination combinations, modulo $1,000,000,007$.

Input

Inputs will be given by standard input in following format

$N$ $l_1$ $r_1$ $l_2$ $r_2$ : $l_N$ $r_N$

• At the first line, an integer $N(1≦N≦2,000)$ will be given divided by a space.
• From the second line there are $N$ additional lines to give the information about the illumination range. For the $i_{th}$ line, integer $l_i$, $r_i(0≦l_i<r_i≦1,000,000,000)$ will be given divided by a space.

Output

Please answer the number of the different illumination combinations, modulo $1,000,000,007$.

Print a newline at the end of output.

Input Example 1

4
0 1
1 2
0 2
1 3

Output Example 1

6

There are $16$ different ways of attaching the light power, but there are only $6$ different illumination combinations, $\\{φ\\}, \\{\[0, 1\]\\}, \\{\[1, 2\]\\}, \\{\[0, 2\]\\}, \\{\[1, 3\]\\}, \\{\[0, 3\]\\}$.

Input Example 2

12
0 4
7 12
1 3
6 8
2 3
4 6
8 9
2 7
9 11
1 2
3 5
7 9

Output Example 2

240

Input Example 3

14
0 1
2 3
4 5
6 7
8 9
10 11
12 13
14 15
16 17
18 19
0 3
4 7
8 13
14 19

Output Example 3

2025