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.

What is Hamming distance?

The Hamming distance between $01$-sequences $X = X_1X_2\\ldots X_N$ and $Y = Y_1Y_2\\ldots Y_N$ is the number of integers $1 \\leq i \\leq N$ such that $X_i \\neq Y_i$.

What is lexicographical order?

A $01$-sequence $X = X_1X_2\\ldots X_N$ is lexicographically smaller than a $01$-sequence $Y = Y_1Y_2\\ldots Y_N$ when there is an integer $1 \\leq i \\leq N$ that satisfies both of the conditions below.

• $X_1X_2\\ldots X_{i-1} = Y_1Y_2\\ldots Y_{i-1}$.
• $X_i =$ 0 and $Y_i =$ 1.

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 $U$.

Sample Input 1

5
00100
10011

Sample Output 1

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.

Sample Input 2

1
0
1

Sample Output 2

-1

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