## MULTQ3 - Multiples of 3

There are N numbers a[0], a[1] ... a[N - 1]. Initially all are 0. You have to perform two types of operations :

- Increase the numbers between indices A and B (inclusive) by 1. This is represented by the command "0 A B"
- Answer how many numbers between indices A and B (inclusive) are divisible by 3. This is represented by the command "1 A B".

### Input

The first line contains two integers, N and Q. Each of the next Q lines are either of the form "0 A B" or "1 A B" as mentioned above.

### Output

Output 1 line for each of the queries of the form "1 A B" containing the required answer for the corresponding query.

### Sample

Input:4 7 1 0 3 0 1 2 0 1 3 1 0 0 0 0 3 1 3 3 1 0 3Output:4 1 0 2

### Constraints

1 ≤ N ≤ 100000

1 ≤ Q ≤ 100000

0 ≤ A ≤ B ≤ N - 1

Added by: | Varun Jalan |

Date: | 2010-09-12 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: NODEJS OBJC VB.NET |

Resource: | own problem |