P1473 [USACO2.3] Zero Sum

Consider an increasing sequence of numbers from $1$ to $N$: $1, 2, 3, \ldots, N$. Insert `+` for addition, `-` for subtraction, or ` ` (a space) for blank between each pair of consecutive numbers (for example, `1-2 3` equals `1-23`). Do not insert any symbol before the first number. Evaluate the resulting expression and determine whether its value is $0$. Write a program to find all expressions of length $N$ whose value is zero.

A single line containing an integer $N$ ($3 \leq N \leq 9$).

In ASCII order, output all expressions obtained by inserting `+`, `-`, or ` ` (space) between each pair of consecutive numbers such that the resulting expression evaluates to $0$. Print one expression per line.

Translated from NOCOW. USACO 2.3. Translated by ChatGPT 5