Problem: Ujan has a lot of numbers in his boxes. He likes order and balance, so he decided to reorder the numbers.

There are k boxes numbered from 1 to k. The i-th box contains n_i integer numbers. The integers can be negative. All of the integers are distinct.

Ujan is lazy, so he will do the following reordering of the numbers exactly once. He will pick a single integer from each of the boxes, k integers in total. Then he will insert the chosen numbers — one integer in each of the boxes, so that the number of integers in each box is the same as in the beginning. Note that he may also insert an integer he picked from a box back into the same box.

Ujan will be happy if the sum of the integers in each box is the same. Can he achieve this and make the boxes perfectly balanced, like all things should be?

Input

The first line contains a single integer k (1 ≤ k ≤ 15), the number of boxes. 

The i-th of the next k lines first contains a single integer n_i (1 ≤ n_i ≤ 5 000), the number of integers in box i. Then the same line contains n_i integers a_{i,1}, …, a_{i,n_i} (|a_{i,j}| ≤ 10^9), the integers in the i-th box. 

It is guaranteed that all a_{i,j} are distinct.

Output

If Ujan cannot achieve his goal, output "No" in a single line. Otherwise in the first line output "Yes", and then output k lines. The i-th of these lines should contain two integers c_i and p_i. This means that Ujan should pick the integer c_i from the i-th box and place it in the p_i-th box afterwards.

If there are multiple solutions, output any of those.

You can print each letter in any case (upper or lower).

Examples

Input


4
3 1 7 4
2 3 2
2 8 5
1 10


Output


Yes
7 2
2 3
5 1
10 4


Input


2
2 3 -2
2 -1 5


Output


No


Input


2
2 -10 10
2 0 -20


Output


Yes
-10 2
-20 1

Note

In the first sample, Ujan can put the number 7 in the 2nd box, the number 2 in the 3rd box, the number 5 in the 1st box and keep the number 10 in the same 4th box. Then the boxes will contain numbers \{1,5,4\}, \{3, 7\}, \{8,2\} and \{10\}. The sum in each box then is equal to 10.

In the second sample, it is not possible to pick and redistribute the numbers in the required way.

In the third sample, one can swap the numbers -20 and -10, making the sum in each box equal to -10.

Solution (in JAVA):

Solution:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
What do you think? What do you think?
1st on Billboard, what do you think of it
Next is a Grammy, what do you think of it
However you think, I’m sorry, but shit, I have no fcking interest
*******************************
I'm standing on top of my Monopoly board
That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300iq as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1242C2
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         long[] sums = new long[N];
         ArrayList<Integer>[] boxes = new ArrayList[N];
         for(int i=0; i < N; i++)
         {
            boxes[i] = new ArrayList<Integer>();
            st = new StringTokenizer(infile.readLine());
            int a = Integer.parseInt(st.nextToken());
            while(a-->0)
               boxes[i].add(Integer.parseInt(st.nextToken()));
            for(int x: boxes[i])
               sums[i] += x;
         }
         long lmaosum = 0L;
         for(long x: sums)
            lmaosum += x;
         if(Math.abs(lmaosum)%N != 0)
         {
            System.out.println("No");
            return;
         }
         long target = lmaosum/N;
         //fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck
         HashMap<Long, Integer> map = new HashMap<Long, Integer>();
         for(int k=0; k < N; k++)
            for(int x: boxes[k])
               map.put((long)x, k);
         HashMap<Long, Long> edges = new HashMap<Long, Long>();
         for(int k=0; k < N; k++)
            for(int x: boxes[k])
            {
               long nextval = target-sums[k]+x;
               if(map.containsKey(nextval))
                  edges.put((long)x, nextval);
            }
         Node[] dp = new Node[1<<N];
         dp[0] = new Node(-69, -69, 0);
         //precompute subsets ass
         Node[] subsets = new Node[1<<N];
         for(int b=0; b < N; b++)
            for(int i=0; i < boxes[b].size(); i++)
            {
               if(!edges.containsKey((long)boxes[b].get(i)))
                  continue;
               long curr = edges.get((long)boxes[b].get(i));
               //shit shit shit shit shit shit shit shit shit shit
               int submask = 0;  boolean cyclic = true;
               while(curr != boxes[b].get(i))
               {
                  int k = map.get(curr);
                  if((submask&(1<<k)) > 0 || !edges.containsKey((long)curr))
                  {
                     cyclic = false;
                     break;
                  }
                  submask |= 1<<k;
                  curr = edges.get((long)curr);
               }
               submask |= (1<<b);
               if(cyclic)
                  subsets[submask] = new Node(-69, i, b);
            }
         for(int mask=1; mask < (1<<N); mask++)
            outer:for(int submask=mask; submask > 0; submask=(submask-1)&mask)
               if(dp[mask^submask] != null && subsets[submask] != null)
               {
                  dp[mask] = new Node(mask^submask, subsets[submask].dex, subsets[submask].start);
                  break outer;
               }
         if(dp[(1<<N)-1] == null)
            System.out.println("No");
         else
         {
            StringBuilder sb = new StringBuilder("Yes\n");
            long[][] res = new long[N][2];
            for(int i=0; i < N; i++)
               res[i][1] = -1L;
            int currmask = (1<<N)-1;
            while(currmask != 0)
            {
               int submask = dp[currmask].mask;
               int i = dp[currmask].dex;
               int b = dp[currmask].start;
               long nextval = target-sums[b]+boxes[b].get(i);
               int curr = map.get(nextval);
               res[map.get(nextval)][0] = nextval;
               res[map.get(nextval)][1] = b;
               while(true)
               {
                  int lol = map.get(nextval);
                  nextval = edges.get(nextval);
                  res[map.get(nextval)][0] = nextval;
                  if(res[map.get(nextval)][1] != -1)
                     break;
                  res[map.get(nextval)][1] = lol;
               }
               currmask = dp[currmask].mask;
            }
            for(int k=0; k < N; k++)
               sb.append(res[k][0]+" ").append(res[k][1]+1).append("\n");
            System.out.print(sb);
         }
      }
   }
   class Node
   {
      public int mask;
      public int dex;
      public int start;
      
      public Node(int a, int b, int c)
      {
         mask = a;
         dex = b;
         start = c;
      }
   }