First In Last Out

Assign distinct hexadecimal digits to the letters in LIST + FILO = STACK so the addition holds, and print every solution in lexicographic order.

Medium4Brute forceBacktrackingMathImplementationNo attempts yetTime limit1sMemory limit32 MB

Description

Examples1

Problem

Assign one hexadecimal digit from $0$ to $f$ to each letter so that the hexadecimal addition $LIST + FILO = STACK$ holds. Different letters must receive different digits, and the leading letters $L$ , $F$ , and $S$ cannot be zero.

Input

There is no input.

Output

Print every valid solution on its own line in lexicographic order. Write each solution in the form $LIST + FILO = STACK$ using hexadecimal digits, with $a$ through $f$ in lowercase. Lexicographic order follows $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f$ .

Hint

Only some solutions are shown to illustrate the output format. A correct program prints every solution that satisfies the conditions.