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 $U$.