This problem deals with Magic Squares that aren't quite magic. Recall that a magic square is a two-dimensional array of numbers such that the sum of each of the elements in each row and in each column are the same. (In some magic squares, the diagonals also sum to the same value as the rows and columns. For this problem, our magic squares do not necesarily share this property.) For example, this 3x3 array

Note: All values (input and output) are integers right-justified in seven-column fields.

For this problem, you are to read a series of 10x10 arrays of integers. The first line of the input contains the number of arrays to be processed. Each array is encoded in 10 input lines, one line per row (hence, each line contains 10 integers).

Each square you read is "not quite magic". That is, the sums do not all equal the same number. Three elements of each square have been modified. One element had the number 1 added to it, another had the number 2 added to it, and a third had the number 4 added to it. Your problem is to find these incorrect elements.

Your program should have five lines for each square. The first line is the magic square value: the correct sum of any row or column. The next three lines contain the row and column number of each of the three incorrect entries in order (off by 1 entry, off by 2 entry, then off by 4 entry). The last of the five lines is blank.

Sample Input

2
      5    252    595    103     45      6    228    476    140    152
    271     82     51    592      5    107    105    137    565     86
     34    465    180    151    173    331    492    111     20     46
    669    162    104     11     55    543    159    198     81     19
     23     41     75    143    723     13     17     78    195    697
    169    133    535     57    106     30     68    719     93     91
    124     35    156    620     65    282    157     60    486     16
    261    618     36     74     12     28    614     98     67    193
    396    189    185     87    144    458    122     77    179    164
     50     26     88    163    673    203     39     47    175    537
      4    252    596    103     45      6    228    476    140    152
    271     84     51    592      5    107    105    137    565     86
     38    463    180    151    173    331    492    111     20     46
    669    162    104     11     55    543    159    198     81     19
     23     41     71    143    723     13     17     78    195    697
    169    133    535     57    106     30     68    719     93     91
    124     35    156    620     65    282    157     60    486     16
    261    618     36     74     12     28    614     98     67    193
    396    189    185     87    144    458    122     77    179    164
     50     26     88    163    673    203     39     47    175    537

Sample Output

2001
1       1
3       2
5       3

2001
1       3
2       2
3       1