From Lewis Carroll¹'s diary, Feb. 5, 1856:

Varied the lesson at the school with a story, introducing a number of sums to be worked out. I also worked for them the puzzle of writing the answer to an addition sum, when only one of the five rows have been written: this … astonished them not a little.

He had started by writing an arbitrary number:

Then he asked the students to call out a second five-digit number. Carroll added a third, the students shouted a fourth, and Carroll added a fifth and immediately wrote the sum:

How did he do this?

Show answer

In writing the third and fifth numbers, he just wrote the complement of 9 for each digit in the number immediately above. When this is done, the sum can be found immediately by taking the first number, subtracting 2 from its last digit, and inserting a 2 at the front of the number.

Assignment

This little trick also works in general for $$1 + m$$ numbers $$x_0, x_1, \ldots, x_m$$, where $$x_0$$ is an $$n$$-digit number and the other numbers have at most $$n$$ digits. First we write down the number $$x_0$$. Then we successively write down the numbers $$x_i$$ and $$c_m(x_i)$$ for $$i = 1, 2, \ldots, m$$. The sum of these numbers is obtained by subtracting $$m$$ from $$x_0$$ and putting the digits of $$m$$ in front.

In the explanation above, we used the $$n$$-complement $$c_n(x)$$ of a number $$x \in \mathbb{N}$$, which is obtained by subtracting $$x$$ from the number that consists of $$n$$ nines. For example, \[ c_5(62593) = 99999 - 62593 = 37406 \] and \[ c_5(82527) = 99999 - 82527 = 17472 \]

Input

A line containing the number $$m \in \mathbb{N}$$ ($$0 \leq m < 100$$). This is followed by another $$1 + m$$ lines containing the numbers $$x_0, x_1, x_2, \ldots, x_m \in \mathbb{N}_0$$ that are written without leading zeros. The number $$x_0$$ has $$n$$ digits (with $$n \geq 3$$) and the numbers $$x_1, x_2, \ldots, x_m$$ have at most $$n$$ digits.

Output

The numbers $$x_0, x_1, c_n(x_1), x_2, c_n(x_2), \ldots, x_m, c_n(x_m)$$, each on a separate line. This is followed by a line containing $$n + 2$$ equal signs (=) and a line containing the result of the sum \[ x_0 + x_1 + c_n(x_1) + x_2 + c_n(x_2) + \cdots + x_m + c_n(x_m) \]

All numbers must be written without leading zeros and must be right aligned across $$n + 2$$ position by adding leading spaces if needed. The line containing the last term of the sum must start with a plus sign (+).

Example

Input:

Output: