Equal Hamming Distances

AtCoder

IDarc151_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ $S$ $T$ [samples]

Samples

Input #1

5
00100
10011

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.

Input #2

1
0
1

Output #2

\-1

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

API Response (JSON)

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    "name": "Equal Hamming Distances",
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      "content": "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 $N$ t",
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    "platform": "AtCoder",
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      "statement_type": "Markdown",
      "content": "Below, a $01$\\-sequence is a string consisting of `0` and `1`.\nYou are given two $01$\\-sequences $S$ and $T$ of length $N$ each. Print the lexicographically smallest $01$\\-sequence $U$ of length $N$ t...",
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