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.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分