Farmer John's son, Johnny is playing with some dominoes one afternoon.
His dominoes come in a variety of heights and colors.

Just like any other child, he likes to put them in a row and knock them over.
He wants to know something: how many pushes does it take to knock down all the dominoes?
Johnny is lazy, so he wants to minimize the number of pushes he takes.
A domino, once knocked over, will knock over any domino that it touches on the way down.

For the sake of simplicity, imagine the floor as a one-dimensional line, where ~1~ is the leftmost point. Dominoes will not slip along the floor once toppled. Also, dominoes do have some width: a domino of length ~1~ at position ~1~ can knock over a domino at position ~2~.

For the mathematically minded:
A domino at position ~x~ with height ~h~, once pushed to the right, will knock all dominoes at positions ~x+1, x+2, \dots, x+h~ rightward as well.
Conversely, the same domino pushed to the left will knock all dominoes at positions ~x-1, x-2, \dots, x-h~ leftward.

Input Specification

The input starts with a single integer ~N \le 100\,000~, the number of dominoes, followed by ~N~ pairs of integers.
Each pair of integers represents the ~\text{location}~ and ~\text{height}~ of a domino.
~(1 \le \text{location} \le 1\,000\,000\,000, 1 \le \text{height} \le 1\,000\,000\,000)~
No two dominoes will be in the same location.

NOTE: ~60\%~ of test data has ~N \le 5\,000~.

Output Specification

One line, with the number of pushes required.

Sample Input

6
1 1
2 2
3 1
5 1
6 1
8 3

Sample Output

2

Push the domino at location ~1~ rightward, the domino at location ~8~ leftward.

Diagram

              |
  |           |
| | |   | |   |
1 2 3 4 5 6 7 8

Pushing ~1~ causes ~2~ and ~3~ to fall, while pushing ~8~ causes ~6~ to fall and gently makes ~5~ tip over as well.