Score : $300$ points

Problem Statement

Below, a $01$-sequence is a string consisting of 0 and 1.

You are given two $01$-sequences $S$ and $T$ of length $N$ each. Print the lexicographically smallest $01$-sequence $U$ of length $N$ that satisfies the condition below.

• The Hamming distance between $S$ and $U$ equals the Hamming distance between $T$ and $U$.

If there is no such $01$-sequence $U$ of length $N$, print $-1$ instead.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $N$ is an integer.
• $S$ and $T$ are $01$-sequences of length $N$ each.

Input

The input is given from Standard Input in the following format:

$N$

$S$

$T$

Output

Print the lexicographically smallest $01$-sequence $U$ of length $N$ that satisfies the condition in the Problem Statement, or $-1$ if there is no such $01$-sequence $U$.

5
00100
10011

00001

For $U =$ 00001, the Hamming distance between $S$ and $U$ and the Hamming distance between $T$ and $U$ are both $2$. Additionally, this is the lexicographically smallest $01$-sequence $U$ of length $N$ that satisfies the condition.

1
0
1

-1

No $01$-sequence $U$ of length $N$ satisfies the condition, so $-1$ should be printed.