Segment Processor

Dilshan is working with a new supercomputer that can run the same program multiple times simultaneously (at the same time). Dilshan has N lists of numbers, and wants to calculate the sum of each number list, using the supercomputer.

He wrote two programs to get this done. mainProgram calls getSumOfSet program N times (simultaneously).

mainProgram accepts 3 parameters.

• S - the length of a single list
• startingPositions - a list containing the starting positions of the N lists
• input - a list containing all the numbers
   

getSumOfSet program accepts 3 parameters.

• S - number of elements to be added from input
• startingPosition - index of the first number in the sequence
• Input - the list containing all the numbers  

mainProgram ( int S, int startingPositions [ ],  int input [ ] ) {
	for each startingPosition in startingPositions:
		call getSumOfSet( S, startingPosition, input )
}

getSumOfSet ( int S, int startingPosition, int input[  ] ) {
	BigInt ans = 0;
	for(int i = 0; i < S; i++) {
		ans += input[ startingPosition + i];
	}
	print ans;
}

Notice that S is the same for all calls to the getSumOfSet program. Hence he needs your help to prepare the input parameters to be sent to mainProgram.

You are allowed to modify the original N lists of numbers in order to meet the input criteria of mainProgram.

Input Format

First line contains a single integer N , the number of lists.
Next line contains N integers, with i ^th of them being C_i .
N lines follow, with the i ^th line having C_i space separated integers and the j ^th of them being V_{i , j} .

Output Format

First line should contain a single integer, S, the length of a number set.
Next line should contain N integers, the starting positions for each number set(startingPositions).
Third line should contain a list of integers (N x S maximum length), the newly prepared list of numbers (input).

Note: the sequence is indexed from 0.

Constraints

• 1 \(\leq\) N \(\leq\) 10⁵
• 1 \(\leq\) C_i \(\leq\) 10³
• -10⁸ \(\leq\) V_{i, j} \(\leq\) 10⁸  

Limits

• Time Limit: 1s
• Memory Limit: 256MB

Sample Input 0

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

Sample Output 0

3
0 3 6 
3 2 1 4 5 6 9 8 7 

Sample Input 1

3
5 2 3
4 3 2 1 0
5 6
9 8 7

Sample Output 1

5
0 5 10 
4 3 2 1 0 5 6 -5 3 2 9 8 7 -8 8 

Sample Input 2

1
5 1000 100 900
10 10
20 10
30 10
40 10
50 10

Sample Output 2

4 800