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→ [10001011]00.
• In the second operation, we can select the prefix of length 2 since it has one 0 and one 1: [10]00101100→ [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)?

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 3⋅ 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⋅ 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).

Example

Input

5 10 0111010000 0100101100 4 0000 0000 3 001 000 12 010101010101 100110011010 6 000111 110100

Output

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.

inputFormat

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 3⋅ 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⋅ 10^5.

outputFormat

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).

Example

Input

5 10 0111010000 0100101100 4 0000 0000 3 001 000 12 010101010101 100110011010 6 000111 110100

Output

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.

样例

5
10
0111010000
0100101100
4
0000
0000
3
001
000
12
010101010101
100110011010
6
000111
110100

YES
YES
NO
YES
NO

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