Adding Sevens

A seven-segment display, like the one shown on the right, is composed of seven light-emitting elements. Each element can be turned on or off individually, allowing for $127$ different combinations, including the ten Arabic numerals. The figure below illustrates how the ten numerals are displayed.

Seven-segment displays (often abbreviated as $7$-seg) are widely used in digital clocks, electronic meters, and calculators.

A $7$-seg display has seven connectors, one for each element, plus a few additional connectors for other electrical purposes. Each element can be turned on by sending an electric current through its pin. Programmers view each of the seven pins as a single bit in a $7$-bit number, as it is more convenient to work with bits rather than electrical signals. The figure below shows the bit assignment for a typical $7$-seg display, with bit $0$ being the rightmost bit.

For example, to display the digit $1$, the programmer knows that only bits $1$ and $3$ must be on. Thus, the $7$-bit binary number for displaying digit $1$ is $0001010$, or $10$ in decimal. We call the decimal number used for displaying a digit its display code, or simply code. Since a $7$-seg display shows $127$ different configurations, display codes are usually written with three decimal digits, using leading zeros when necessary. For instance, the display code for the digit $1$ is written as $010$.

In a $9$-digit calculator, nine $7$-seg displays are placed next to each other and are all controlled by a single controller. The controller is sent a sequence of $3n$ digits, representing $n$ display codes, where 0 < n < 10. If n < 9, the number is right-aligned and leading zeros are automatically displayed. For example, the display code for $13$ is $010079$, while for $144$ it is $010106106$.

Write a program that reads the display codes of two numbers and prints the display code of their sum.