An  elephant  lives by  a  lake with N plants on  the  surface. The  lake  
can be modeled by  a  coordinate plane, with plants at points with 
integer coordinates. 
Every morning  after waking  up,  the  elephant  performs  his 
morning  exercise,  happily  jumping  from plant  to plant. For  
reasons best  left undiscussed,  the elephant can always jump only  to 
another plant with both coordinates larger than the coordinates of
the plant it is currently on. In other words, from plant (x1, y1) the 
elephant can jump to plant (x2, y2) only if x2 > x1 and y2 > y1. 
The elephant can start his exercise at any plant on the lake. 
Write a program that, given the coordinates of all plants, calculates
the length of the longest sequence of  plants  the  elephant  can  visit.  
Additionally,  calculate  the  number  of  different  such  longest 
sequences. Because this second number can be large, calculate it 
modulo 1 000 000 007.  

Input

The first line contains the integer N (1 ≤ N ≤ 300 000), the number of plants. 
Each of the following N  lines contains the coordinates of one plant, 
two  integers between 0 and 10^9.
No two plants will have the same pair of coordinates. 

Output

On the first line output the length of the longest sequence of plants
the elephant can jump on. 
On the second line output the number of such sequences of maximum length, 
modulo 1 000 000  007. 

Sample

Sample input
input 
11 
8 6 
7 4 
5 4 
5 1 
5 6 
6 2 
3 2 
4 3 
4 5 
3 5 
2 4 
output 
4 
3 

input 
6 
1 3 
2 2 
3 1 
5 3 
4 4 
3 5 
output 
2 
7