Bailey is given a number in form of its binary representation S, having length N. Determine if the number can be represented as a sum of exactly three powers of 2. Please refer to samples for further explanation. Note that S will NOT contain leading zeros. Input Format The first line of input will contain a single integer T, denoting the number of test cases. Each test case consists of multiple lines of input. The first line of each test case contains a single integer N, the length of the binary string. The next line contains the string S, the binary representation of a number. Output Format For each test case, output YES if the number can be represented as sum of exactly three powers of 2.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Bailey is given a number in form of its binary representation S, having length N.

Determine if the number can be represented as a sum of exactly three powers of 2. Please refer to samples for further explanation.

Note that S will NOT contain leading zeros.

Input Format

  • The first line of input will contain a single integer T, denoting the number of test cases.
  • Each test case consists of multiple lines of input.
    • The first line of each test case contains a single integer N, the length of the binary string.
    • The next line contains the string S, the binary representation of a number.

Output Format

For each test case, output YES if the number can be represented as sum of exactly three powers of 2.

Constraints

  • 1≤T≤1000
  • 1≤N≤2⋅105
  • S consists of 0 and 1 only, and has no leading zeros.
  • The sum of N over all test cases won't exceed 2⋅105.

Sample:

 
INPUT OUTPUT
4 NO
1 YES
1 YES
4 NO
1001  
5  
11001  
7  
1101101  

Explanation:

Test case 1: It is not possible to represent the given number as a sum of exactly three powers of 2.

Test case 2: The given string 1001 corresponds to the number 9. We can represent 9 as a sum of exactly three powers of 2 as 9=22+22+20.

Test case 3: The given string 11001 corresponds to the number 25. We can represent 25 as a sum of exactly three powers of 2 as 25=24+23+20.

Test case 4: It is not possible to represent the given number as a sum of exactly three powers of 2.

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