Codeforces Global Round 6 |
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Finished |

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chinese remainder theorem

math

*1000

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A. Competitive Programmer

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBob is a competitive programmer. He wants to become red, and for that he needs a strict training regime. He went to the annual meeting of grandmasters and asked $$$n$$$ of them how much effort they needed to reach red.

"Oh, I just spent $$$x_i$$$ hours solving problems", said the $$$i$$$-th of them.

Bob wants to train his math skills, so for each answer he wrote down the number of minutes ($$$60 \cdot x_i$$$), thanked the grandmasters and went home. Bob could write numbers with leading zeroes — for example, if some grandmaster answered that he had spent $$$2$$$ hours, Bob could write $$$000120$$$ instead of $$$120$$$.

Alice wanted to tease Bob and so she took the numbers Bob wrote down, and for each of them she did one of the following independently:

- rearranged its digits, or
- wrote a random number.

This way, Alice generated $$$n$$$ numbers, denoted $$$y_1$$$, ..., $$$y_n$$$.

For each of the numbers, help Bob determine whether $$$y_i$$$ can be a permutation of a number divisible by $$$60$$$ (possibly with leading zeroes).

Input

The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 418$$$) — the number of grandmasters Bob asked.

Then $$$n$$$ lines follow, the $$$i$$$-th of which contains a single integer $$$y_i$$$ — the number that Alice wrote down.

Each of these numbers has between $$$2$$$ and $$$100$$$ digits '0' through '9'. They can contain leading zeroes.

Output

Output $$$n$$$ lines.

For each $$$i$$$, output the following. If it is possible to rearrange the digits of $$$y_i$$$ such that the resulting number is divisible by $$$60$$$, output "red" (quotes for clarity). Otherwise, output "cyan".

Example

Input

6 603 006 205 228 1053 0000000000000000000000000000000000000000000000

Output

red red cyan cyan cyan red

Note

In the first example, there is one rearrangement that yields a number divisible by $$$60$$$, and that is $$$360$$$.

In the second example, there are two solutions. One is $$$060$$$ and the second is $$$600$$$.

In the third example, there are $$$6$$$ possible rearrangments: $$$025$$$, $$$052$$$, $$$205$$$, $$$250$$$, $$$502$$$, $$$520$$$. None of these numbers is divisible by $$$60$$$.

In the fourth example, there are $$$3$$$ rearrangements: $$$228$$$, $$$282$$$, $$$822$$$.

In the fifth example, none of the $$$24$$$ rearrangements result in a number divisible by $$$60$$$.

In the sixth example, note that $$$000\dots0$$$ is a valid solution.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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