Number Pairs

Given a natural number $N$, write a program that finds every pair of numbers $(X, Y)$ such that $X + Y = N$. Here $Y$ must be a number obtained by deleting exactly one digit from the decimal representation of $X$.

• $X$ is a natural number with at least two digits and may not start with $0$.
• $Y$ has at least one digit; if the deleted digit was the leading one, $Y$ may start with $0$. Consequently $Y$ always has exactly one fewer digit than $X$.

For example, deleting the leading digit $3$ from $X = 301$ gives $Y = 01$, and $301 + 01 = 302$.

The first line contains a natural number $N$. ($10 \le N \le 10^9$)

On the first line, print the number of distinct pairs that satisfy the condition.

From the next line, print each valid pair on its own line in increasing order of $X$. Each line has the form X + Y = N, where $X$, $Y$, and $N$ are replaced by the actual numbers and exactly one space surrounds each + and = sign. Print $Y$ exactly as it appears after the digit deletion, so it may keep a leading $0$ when the deleted digit was the first one.