Dr. Anne Anderson has ~N~ different courses, numbered ~1~ to ~N~. Some of those courses have prerequisites, defined by ~M~ prerequisite pairs. For each pair, course ~A_i~ is a prerequisite of course ~B_i~, meaning that course ~A_i~ must be completed in a semester strictly before course ~B_i~. A course can be a prerequisite for multiple courses, and a course can have multiple different prerequisites.

Ratish had his heart set on taking ~K~ specific courses, and he's willing to take any number of courses per semester. However, he wants to follow a few rules with his schedule:

• He wants to finish all of his requested courses in as few semesters as possible.

• He doesn't want to take any courses that he doesn't need to.

• He wants to take each of the courses that he must take in the earliest semester possible.

Given his requirements, Ratish asks you to create a high school plan for him. He wants you to tell him the minimum number of semesters he needs to be in school, ~X~. He also wants you to tell him the courses he should take in each semester to finish high school in ~X~ semesters. To make it easier for him, he also wants you to sort the courses he should take in each semester. Can you write a program to help him?

Constraints

~1 \leq K \leq N \leq 2 \times 10^5~

~0 \leq M \leq 2 \times 10^5~

~1 \leq A_i, B_i \leq N~

No course is a direct or indirect prerequisite of itself.

There are no duplicate prerequisite pairs.

Subtask 1 [25%]

Each course has one or less prerequisites, and is the prerequisite of one or less courses.

Subtask 2 [35%]

~K = N~

Subtask 3 [40%]

No additional constraints.

Input Specification

The first line contains the integer ~N~.

The second line contains the integer ~M~.

The third line contains the integer ~K~.

The fourth line contains ~K~ integers separated by spaces, the courses that Ratish wants to take.

The next ~M~ lines contain the integers ~A_i~ and ~B_i~, indicating that course ~A_i~ is a prerequisite of course ~B_i~.

Output Specification

The first line contains the integer ~X~.

For the following ~X~ lines, line ~i~ contains all of the courses taken in semester ~i~, separated by spaces.

Sample Input 1

6
4
2
1 2
5 4
3 1
3 2
4 2

Sample Output 1

3
3 5
1 4
2

Explanation For Sample 1

Ratish wants to take courses 1 and 2. The most optimal way to do this would be to take courses 3 and 5 in semester 1, courses 1 and 4 in semester 2, and course 2 in semester 3.

Ratish does not need to take course 6 in order to take his desired courses.

Sample Input 2

9
9
3
2 1 3
4 6
3 5
6 5
6 7
5 1
7 1
6 2
1 8
5 9

Sample Output 2

4
3 4
6
2 5 7
1

Explanation for Sample 2

Course 2 can be completed in either semester 3 or 4 to complete high school in 4 semesters. However, Ratish wants to complete each of his required courses as soon as possible, so course 2 must be completed in semester 3.