In March 1955, Pedro A. Pisa discovered this unkillably valid equation:

123789 + 561945 + 642864 = 242868 + 323787 + 761943

Hack away at its terms — from either end — and it remains true:

1      + 5      + 6      = 2      + 3      + 7
12     + 56     + 64     = 24     + 32     + 76
123    + 561    + 642    = 242    + 323    + 761
1237   + 5619   + 6428   = 2428   + 3237   + 7619
12378  + 56194  + 64286  = 24286  + 32378  + 76194
123789 + 561945 + 642864 = 242868 + 323787 + 761943
 23789 +  61945 +  42864 =  42868 +  23787 +  61943
  3789 +   1945 +   2864 =   2868 +   3787 +   1943
   789 +    945 +    864 =    868 +    787 +    943
    89 +     45 +     64 =     68 +     87 +     43
     9 +      5 +      4 =      8 +      7 +      3

Stab it in the heart, removing the two center digits from each term, and it still balances:

1289 + 5645 + 6464 = 2468 + 3287 + 7643

Do this again and it still balances:

19 + 55 + 64 = 28 + 37 + 73

Most amazing: you can square every term above, in every equation, and they'll all remain true.

Input

Six $$n$$-digit numbers ($$n \in \mathbb{N}_0$$) that do not contain the digit zero (0), each on a separate line.

Output

Each line of the output contains an equation whose left-hand side sums part of the digits of the first three numbers from the input and whose right-hand side sums part of the digits of the last three numbers from the input. The parts successively consist of

the first $$i$$ digits from each term ($$i = 1, \ldots n - 1$$; left aligned)
all digits from each term
the last $$i$$ digits from each term ($$i = n - 1, \ldots 1$$; right aligned)

Place an equality sign (=) or an inequality sign (≠) between the left-hand side and the right-hand side of each equation to indicate whether or not the equation holds. Put one space before and after each plus sign (+), equality sign (=) and inequality sign (≠).

The terms must be aligned across $$n$$ positions by adding leading or trailing spaces. There should never be spaces at the end of a line.

Example

Input:

Output:

1      + 5      + 6      = 2      + 3      + 7
12     + 56     + 64     = 24     + 32     + 76
123    + 561    + 642    = 242    + 323    + 761
1237   + 5619   + 6428   = 2428   + 3237   + 7619
12378  + 56194  + 64286  = 24286  + 32378  + 76194
123789 + 561945 + 642864 = 242868 + 323787 + 761943
 23789 +  61945 +  42864 =  42868 +  23787 +  61943
  3789 +   1945 +   2864 =   2868 +   3787 +   1943
   789 +    945 +    864 =    868 +    787 +    943
    89 +     45 +     64 =     68 +     87 +     43
     9 +      5 +      4 =      8 +      7 +      3

Example

Input:

Output:

1    + 9    + 3    = 2    + 7    + 4
19   + 93   + 31   = 22   + 73   + 48
195  + 933  + 311  ≠ 221  + 736  + 483
1959 + 9336 + 3117 = 2216 + 7361 + 4835
 959 +  336 +  117 =  216 +  361 +  835
  59 +   36 +   17 =   16 +   61 +   35
   9 +    6 +    7 ≠    6 +    1 +    5

Epilogue

In 2016, Jean-Claude Georges discovered that the equalities remain valid when any combination of digits is removed consistently across terms. For example, starting from

123789 + 561945 + 642864 = 242868 + 323787 + 761943

and removing the first, third and fifth digit from each number

123789 + 561945 + 642864 = 242868 + 323787 + 761943

gives

279 + 695 + 484 = 488 + 277 + 693 (= 1458)

and squaring each term gives

77841 + 483025 + 234256 = 238144 + 76729 + 480249 (= 795122)

Amazingly, the same is true for any combination — for example, the equations remain valid when the first, second, fourth, and sixth digits of each term are removed.