Palindrome Flipping Codechef Solution

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Palindrome Flipping Codechef Solution

Palindrome Flipping Codechef Solution

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Problem

Chef has a binary string S of length N.

In one operation, Chef can:

  • Select two indices i and j (1 \le i, j \le N) and flip S_i and S_j. (i.e. change 0 to 1 and 1 to 0)

For example, if S = 10010 and chef applys operation on i = 1 and j = 3 then: \underline{1}0\underline{0}10 \rightarrow 00110.

Find if it is possible to convert S to a palindrome by applying the above operation any (possibly zero) number of times.

Note: A string is called a palindrome if it reads the same backwards and forwards, for e.g. 10001 and 0110 are palindromic strings.

Input Format

  • The first line contains a single integer T — the number of test cases. Then the test cases follow.
  • The first line of each test case contains an integer N — the length of the binary string S.
  • The second line of each test case contains a binary string S of length N containing 0s and 1s only.

Output Format

For each test case, output YES if it is possible to convert S to a palindrome. Otherwise, output NO.

You can print each character of the string in uppercase or lowercase. For example, the strings YESyesYes, and yEs are all considered the same.

Constraints

  • 1 \leq T \leq 10^5
  • 1 \leq N \leq 10^5
  • S contains 0 and 1 only.
  • Sum of N over all test cases does not exceed 2 \cdot 10^5.

Sample 1:

Input

Output

3
6
101011
2
01
7
1110000
YES
NO
YES

Explanation:

Test case 1: We can perform the following operation:

  • Select i = 3 and j = 5. Then 10\underline{1}0\underline{1}1 \rightarrow 100001, which is a palindrome.

Test case 2: It can be proven that we can not make S a palindrome using the given operation.

Test case 3: We can perform the following operations:

  • Select i = 4 and j = 5. Then 111\underline{0}\underline{0}00 \rightarrow 1111100
  • Select i = 6 and j = 7. Then 11111\underline{0}\underline{0} \rightarrow 1111111, which is a palindrome.
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SOLUTION

Palindrome Flipping Codechef Solution

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