Problem Statement

There are ~N~ cities numbered ~1, \dots, N~ , and ~M~ roads connecting cities.
The ~i~ -th road ~(1 \leq i \leq M)~ connects city ~A_i~ and city ~B_i~ .

Print ~N~ lines as follows.

• Let ~d_i~ be the number of cities directly connected to city ~i \, (1 \leq i \leq N)~ , and those cities be city ~a_{i, 1}~ , ~\dots~ , city ~a_{i, d_i}~ , in ascending order .
• The ~i~ -th line ~(1 \leq i \leq N)~ should contain ~d_i + 1~ integers ~d_i, a_{i, 1}, \dots, a_{i, d_i}~ in this order, separated by spaces.

Constraints

• ~2 \leq N \leq 10^5~
• ~1 \leq M \leq 10^5~
• ~1 \leq A_i \lt B_i \leq N \, (1 \leq i \leq M)~
• ~(A_i, B_i) \neq (A_j, B_j)~ if ~(i \neq j)~ .
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~ ~M~ ~A_1~ ~B_1~ ~\vdots~ ~A_M~ ~B_M~

Output

Print ~N~ lines as specified in the Problem Statement.

Sample Input 1

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

Sample Output 1

3 2 3 6
2 1 5
2 1 6
0
2 2 6
3 1 3 5

The cities directly connected to city ~1~ are city ~2~ , city ~3~ , and city ~6~ . Thus, we have ~d_1 = 3, a_{1, 1} = 2, a_{1, 2} = 3, a_{1, 3} = 6~ , so you should print ~3, 2, 3, 6~ in the first line in this order, separated by spaces.

Note that ~a_{i, 1}, \dots, a_{i, d_i}~ must be in ascending order. For instance, it is unacceptable to print ~3, 3, 2, 6~ in the first line in this order.

Sample Input 2

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 2

4 2 3 4 5
4 1 3 4 5
4 1 2 4 5
4 1 2 3 5
4 1 2 3 4