Olympiad in Informatics

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:

1. 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?
2. 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

Input
13 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 8

Output
yes
yes
yes
no
yes