#P1504B. Flip the Bits
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ID: 5845
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Flip the Bits
No submission language available for this problem.
Description
There is a binary string $a$ of length $n$. In one operation, you can select any prefix of $a$ with an equal number of $0$ and $1$ symbols. Then all symbols in the prefix are inverted: each $0$ becomes $1$ and each $1$ becomes $0$.
For example, suppose $a=0111010000$.
- In the first operation, we can select the prefix of length $8$ since it has four $0$'s and four $1$'s: $[01110100]00\to [10001011]00$.
- In the second operation, we can select the prefix of length $2$ since it has one $0$ and one $1$: $[10]00101100\to [01]00101100$.
- It is illegal to select the prefix of length $4$ for the third operation, because it has three $0$'s and one $1$.
Can you transform the string $a$ into the string $b$ using some finite number of operations (possibly, none)?
The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1\le n\le 3\cdot 10^5$) — the length of the strings $a$ and $b$.
The following two lines contain strings $a$ and $b$ of length $n$, consisting of symbols $0$ and $1$.
The sum of $n$ across all test cases does not exceed $3\cdot 10^5$.
For each test case, output "YES" if it is possible to transform $a$ into $b$, or "NO" if it is impossible. You can print each letter in any case (upper or lower).
Input
The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1\le n\le 3\cdot 10^5$) — the length of the strings $a$ and $b$.
The following two lines contain strings $a$ and $b$ of length $n$, consisting of symbols $0$ and $1$.
The sum of $n$ across all test cases does not exceed $3\cdot 10^5$.
Output
For each test case, output "YES" if it is possible to transform $a$ into $b$, or "NO" if it is impossible. You can print each letter in any case (upper or lower).
Samples
5
10
0111010000
0100101100
4
0000
0000
3
001
000
12
010101010101
100110011010
6
000111
110100
YES
YES
NO
YES
NO
Note
The first test case is shown in the statement.
In the second test case, we transform $a$ into $b$ by using zero operations.
In the third test case, there is no legal operation, so it is impossible to transform $a$ into $b$.
In the fourth test case, here is one such transformation:
- Select the length $2$ prefix to get $100101010101$.
- Select the length $12$ prefix to get $011010101010$.
- Select the length $8$ prefix to get $100101011010$.
- Select the length $4$ prefix to get $011001011010$.
- Select the length $6$ prefix to get $100110011010$.
In the fifth test case, the only legal operation is to transform $a$ into $111000$. From there, the only legal operation is to return to the string we started with, so we cannot transform $a$ into $b$.