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#### Description

Different countries use different coin denominations. For example, the USA uses 1, 5, 10, and
25. A desirable property of coin denominations is to have each coin at least twice the amount of
its previous coin in sorted order. For example, the USA denominations have this property, but
the coin denominations {1, 5, 6} do not (6 is not at least twice 5).
The Problem:
Given the coin denominations, you are to determine if the set has the above property.

#### Input

The first input line contains a positive integer, n, indicating the number of denomination sets to
check. The sets are on the following n input lines, one set per line. Each set starts with an
integer d (1 ≤ d ≤ 10), which is a count of various coin amounts in the set; this is followed by d
distinct positive integers (each less than 1,000) giving each coin amount (assume the coin
amounts are given in increasing order).

#### Output

At the beginning of each test case, output “Denominations: v” where v is the input values.
Then, on the next output line, print a message indicating whether or not the set has the above
property. Leave a blank line after the output for each test case. Follow the format illustrated in
Sample Output.

#### Samples

Input Copy
2
4 1 5 10 25
3 1 5 6
Output
Denominations: 1 5 10 25
Good coin denominations!

Denominations: 1 5 6


#### Source

UCF2011
##### Problem Information

 Time Limit: 1000MS (C/C++,Others×2) Memory Limit: 128MB (C/C++,Others×2) Special Judge: No AC/Submit: 1 / 1 Tags:
##### Contests involved

 1023. UCF 2011