CPDUEL5A - Comet Number
A positive integer X is a comet number if there exists 5 positive integers A B C D E such that:
- A + B + C + D = X
- A + E, B - E, C * E, and D / E are pairwise equal, meaning A + E = B - E = C * E = D / E
Kanata gave Suisei N positive integers Ai for 1 ≤ i ≤ N.
Suisei would like to know whether Ai is a comet number or not.
Input
The first line contains an integer N.
The next N lines contain an integer Ai.
Output
Print N lines.
The i-th line contains the string "YES" (without quotes) if Ai is a comet number and "NO" (without quotes) otherwise.
Example
Input: 4 8 1 69 128 Output: YES NO NO YES
Explanation
8 is a comet number as there exists a valid quintuple (A, B, C, D, E) = (1, 3, 2, 2, 1).
128 is a comet number as there exists a valid quintuple (A, B, C, D, E) = (31, 33, 32, 32, 1).
Constraints
1 ≤ N, Ai ≤ 105
hide comments
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Waseem Ahmed:
2021-08-27 06:55:41
Thanks for the hints @@sachinverma and @robosapien |
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Sachin verma:
2021-01-02 19:47:33
Simple maths and loop. Also, might be obvious but watch out for the "positive integers" bit, costed me few WAs. |
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robosapien:
2020-11-26 20:16:08
nice problem.. just one observation does the job. :) |
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Sushovan Sen:
2020-11-09 08:54:44
@nadstratosfer please try to keep one successful submission per user. Otherwise it dilutes points gained for other users. It may not matter for you but it may matter for somebody else.
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nadstratosfer:
2020-11-08 17:17:18
1) Please replace Ai with X for simplicity and consistency.
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| Added by: | Maximilliano |
| Date: | 2020-11-05 |
| Time limit: | 1s |
| Source limit: | 50000B |
| Memory limit: | 1536MB |
| Cluster: | Cube (Intel G860) |
| Languages: | All |
| Resource: | Own Problem |
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