I :: Intervals

Time Limit: 2 Seconds    Memory Limit: 32768 KB

There are a lot of lamps in Mollasadra street. Each lamp has a height h and a coordinate x. Babak wants to find the interval (x1, x2) with the maximum lightness (excluding x1 and x2). An interval has a more lightness if there are more lamps to lighten it. Each lamp lightens a symmetric range around x as long as h/2 from each side. You need to find the number of the intervals with the maximum lightness.


There are multiple test cases. Each one begins with an integer n1000 as the number of lamps followed by n lines. The ith line contains two integers  xi and hi denotes coordinate and height of ith lamp (absolute value of each integer is less than 109 and hi>0 is even for each i).


For each test case, print two integers. The number of intervals with the maximum lightness and the number of lamps lighten each one.

Sample Input

2 4
3 6
1 2
2 4
3 2

Sample Output

1 2
2 2

Source: 12th Iran Nationwide Internet Contest IV