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, ..., x+h rightward as well.
Conversely, the same domino pushed to the left will knock all dominoes at positions x-1, x-2, ..., x-h leftward.


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

NOTE: 60% of test data has N ≤ 5000.


One line, with the number of pushes required.

Sample Input

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

Sample Output


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


  |           |
| | |   | |   |
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.

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Best Solutions

Point Value: 25
Time Limit: 1.00s
Memory Limit: 64M
Added: Sep 26, 2008
Author: hansonw1

Problem Types: [Show]

Languages Allowed:

Comments (Search)

Try solving it in O(n^2) complexity, then you can convert it to O(N*LOG(N)) using Data structure.

The dominos aren't sorted by position.

Make a recursive function f(n) that gives the minimum # of moves required to topple the first n dominoes.

Now how do you relate f(n) to previous values of f?
Domino #n has two choices: go left (in which case it topples other dominoes over) or go right
(in which case another domino to its left topples it over). Try working from there.