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.

Input

There are multiple test cases. Each one begins with an integer n≤1000 as the number of lamps followed by n lines. The i^th line contains two integers  x_i and h_i denotes coordinate and height of i^th lamp (absolute value of each integer is less than 10⁹ and h_i>0 is even for each i).

Output

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
2 4
3 6
3
1 2
2 4
3 2

Sample Output

1 2
2 2

Submit

Source: 12th Iran Nationwide Internet Contest IV