## CORRAL - Covering the Corral

The cows are so modest they want Farmer John to install covers around the circular corral where they occasionally gather. The corral has circumference C (1 <= C <= 1,000,000,000), and FJ can choose from a set of M (1 <= M <= 100,000) covers that have fixed starting points and sizes. At least one set of covers can surround the entire corral.

Cover i can be installed at integer location x_i (distance from starting point around corral) (0 <= x_i < C) and has integer length l_i (1 <= l_i <= C).

FJ wants to minimize the number of segments he must install. What is the minimum number of segments required to cover the entire circumference of the corral?

Consider a corral of circumference 5, shown below as a pair of connected line segments where both '0's are the same point on the corral (as are both 1's, 2's, and 3's).

Three potential covering segments are available for installation:

```
Start Length
i x_i l_i
1 0 1
2 1 2
3 3 3
0 1 2 3 4 0 1 2 3 ...
corral: +---+---+---+---+--:+---+---+---+- ...
1111 1111
22222222 22222222
333333333333
|..................|
```

As shown, installing segments 2 and 3 cover an extent of (at least) five units around the circumference. FJ has no trouble with the overlap, so don't worry about that.

### Input:

- Line 1: Two space-separated integers: C and M.
- Lines 2..M+1: Line i+1 contains two space-separated integers: x_i and l_i

### Output:

- Line 1: A single integer that is the minimum number of segments required to cover all segments of the circumference of the corral.

### Sample

Input5 3 0 1 1 2 3 3Output2

Added by: | sieunhan |

Date: | 2011-03-21 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | Usaco Feb10 Gold |