# domino

Dominos with different heights
`(x`_{1},h_{1}),...,(x_{N},h_{N})

are
standing on the `x`

-axis. Every domino stands in a way that its
base is perpendicular to the axis and the axis goes through the center of its base.
The `x`

coordinate and the height of the `k`

-th domino
are `x`_{k}

and `h`_{k} (k=1...N)

respectively.
No two dominos have the same `x`

coordinate. Pushing the
domino `(x`_{k},h_{k})

to the right (to the positive direction)
will cause *directly* the fall of the dominos to its right whose distance
from `x`_{k}

is strictly smaller than `h`_{k}

.
Similarly, pushing this domino to the left will cause *directly* the fall of
the dominos to its left whose distance from `x`_{k}

is
strictly smaller than `h`_{k}

.
Clearly, it can cause the fall of other dominos indirectly.

What is the maximal number (`M`

) of dominos that will fall by choosing
at most `2`

dominos, and pushing them independently to the right or
to the left?

## Example 1

x h
10 10
16 5
18 2
20 5

By pushing the domino `(10,10)`

to the right, every domino will fall,
therefore `M=4`

.

## Example 2

x h
0 3
2 1
10 3
8 3
100 1
-1000 1

By pushing `(0,3)`

to the right and `(10,3)`

to the left
4 dominos will fall, and no way to get more, therefore `M=4`

.

## Example 3

x h
-7 1
-5 3
-1 5
1 5
5 3
7 1

Every domino will fall by pushing `(-1,5)`

to the left and `(1,5)`

to the right.

## Input Specification

N
x_{1} h_{1}
...
x_{N} h_{N}

The first line is the number ` 1 ≤ N ≤ 10`^{5}

.
In the next `N`

lines, the space separated
` -10`^{8} ≤ x_{k} ≤ 10^{8}

and
` 1 ≤ h`_{k} ≤ 10^{8}

come, `k=1...N`

.

## Output Specification

M

A single line with the required `M`

.

## Sample Input 1

`4`

`16 5`

`20 5`

`10 10`

`18 2`

download as text file
## Sample Output 1

`4`

download as text file
## Sample Input 2

`6`

`0 3`

`2 1`

`10 3`

`8 3`

`100 1`

`-1000 1`

download as text file
## Sample Output 2

`4`

download as text file
## Sample Input 3

`4`

`1 1`

`2 1`

`3 1`

`4 1`

download as text file
## Sample Output 3

`2`

download as text file