A14247 | Flip the Bits

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).