## NKPOLICE - Police

English | Vietnamese |

To help capture criminals on the run, the police are introducing a new computer system. The area covered by the police contains N cities and E bidirectional roads connecting them. The cities are labelled 1 to N.

The police often want to catch criminals trying to get from one city to another. Inspectors, looking at a map, try to determine where to set up barricades and roadblocks. The new computer system should answer the following two types of queries:

- Consider two cities A and B, and a road connecting cities G1 and G2. Can the criminals get from city A to city B if that one road is blocked and the criminals can't use it?
- Consider three cities A, B and C. Can the criminals get from city A to city B if the entire city C is cut off and the criminals can't enter that city?

Write a program that implements the described system.

### Input

- The first line contains two integers N and E (2 ≤ N ≤ 100 000, 1 ≤ E ≤ 500 000), the number of cities and roads.
- Each of the following E lines contains two distinct integers between 1 and N – the labels of two cities connected by a road. There will be at most one road between any pair of cities.
- The following line contains the integer Q (1 ≤ Q ≤ 300 000), the number of queries the system is being tested on.
- Each of the following Q lines contains either four or five integers. The first of these integers is the type of the query – 1 or 2.
- If the query is of type 1, then the same line contains four more integers A, B, G1 and G2 as described earlier. A and B will be different. G1 and G2 will represent an existing road.
- If the query is of type 2, then the same line contains three more integers A, B and C. A, B and C will be distinct integers.
- The test data will be such that it is initially possible to get from each city to every other city.

### Output

Output the answers to all Q queries, one per line. The answer to a query can be "yes" or "no".

### Example

Input13 15 1 2 2 3 3 5 2 4 4 6 2 6 1 4 1 7 7 8 7 9 7 10 8 11 8 12 9 12 12 13 5 1 5 13 1 2 1 6 2 1 4 1 13 6 7 8 2 13 6 7 2 13 6 8Outputyes yes yes no yes

Added by: | Jimmy |

Date: | 2007-12-27 |

Time limit: | 0.101s-1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | Croatian Open 2006 |