SNGDIV69 - Divisible by 6 and 9

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Let num (> 0) be n (> 0) digit(s) positive integer. num is represented as N1N2N3N4...Nn-2Nn-1Nn, where Ni is the ith digit of num from left (0 < i < n+1). Digits of num are sorted in descending and ascending order respectively and this sorting generates two new positive integers numdsc and numasc. The difference between the numbers is diffnum = numdsc - numasc, if diffnum is divisible by both 6 and 9, then we say that num is a magic number. Let sumdigits be defined as following

    number = diffnum
    do {
        number = sum of digits of number
    } while (number > 10)
    sumdigits = number

Input

First line of input is t (< 101), total number of test cases. Each test case has n (< 10001) as its first input and next n lines contains num (< 10100).

Output

For each test case, write exactly n lines containing two or three specifications without space:

  1. Y if num is magic number otherwise N.
  2. Let sumdigits = c, ZER if c is 0 (zero), ONE if c is 1 (one) if c > 1, EP if c is even and prime, ENP if c is even but not prime, OP if c is odd and prime or ONP if c is odd but not prime.
  3. Let diffnum = d, If num is not a magic number then print EQL if d is not divisible by both 6 and 9, LTN if d is not divisible by 6 only, GTN if d is not divisible by 9 only.

Example

Input:
1
2
31
100

Output:
YONP
NONPLTN

0 is divisible by 6 and 9 :)


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[Lakshman]: 2013-11-16 11:23:00

@Abhimanyu Singh Can you please check my submission.? Getting WA

AvmnuSng: 2013-11-16 11:23:00

Say number is 86373299
Then ascending is 23367899
and descending is 99876332
Simple ...

Mostafa 36a2: 2013-11-16 11:23:00

"Digits of num are sorted in descending and ascending order respectively"
(I dont know if i understand)
is that mean that there is firstly a descending digits then ascending like :
998877654212345577889
or
987789 ?

AvmnuSng: 2013-11-16 11:23:00

diff is always greater than or equal to 0

numerix: 2013-11-16 11:23:00

As num_dsc can not be smaller than num_asc according to the definition of these numbers, diff < 0 is impossible.

Mostafa 36a2: 2013-11-16 11:23:00

What if diff < 0 ?


Added by:AvmnuSng
Date:2013-10-24
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
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