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 integer t — the number of test cases.
The first line of each test case contains integer n — 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).

#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> int main() { int n_cases, n, balance, diff; char s1[300001], s2[300001], *c1, *c2; bool any_same, any_different; scanf("%d", &n_cases); while (n_cases--) { scanf("%d", &n); scanf("%s\n%s", s1, s2); c1 = s1; c2 = s2; any_same = false; any_different = false; balance = 0; diff = 0; while (*c1) { any_same = any_same||*c1==*c2; any_different = any_different||*c1!=*c2; if (any_same && any_different) break; balance += *c2 == '1' ? 1 : -1; diff += *c1 - *c2; if (balance == 0) { any_same = false; any_different = false; } c1++; c2++; } printf(((any_same && any_different)||diff!= 0)?"NO\n" : "YES\n"); } return 0; }

**INPUT_1:**

2

8

00100011

00011001

10

0101010101

0110011010

**OUTPUT:**

NO

YES

**INPUT_2:**

5

4

0000

0000

8

01001010

11110000

3

001

000

12

010101010101

100110011010

6

000111

110100

**OUTPUT:**

YES

NO

NO

YES

NO

**Morae Q!**

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