After finally exchanging phone numbers with Xoranna - *spoilers ;-)* -, Xorin was eager to set up their first date.

So he patiently waited for her call. However, Xorin decided to only answer calls made at times which could be considered peculiar, because he was convinced that such a correlation meant that Xoranna loved (**Accepted**) him. A time is expressed as a 5-character string (**XY:ZT**, where **XY** denotes the hour, and **ZT** - the minutes), and is considered peculiar if any of the following criteria holds:

- It is an exact hour:
**ZT == "00"**(e.g. 12:00) - It is a doubled time:
**XY == ZT**(e.g. 12:12) - It is a mirror time:
**XY == TZ**(e.g. 12:21) - It has increasing consecutive digits (e.g. 01:23, 23:45)
- After removing the separating ":", the remaining 4-digit number is a power of two with no leading zeros (e.g. 10:24, 20:48)

Moreover, it is guaranteed that X, Y, Z, and T will be contained by "0123456789", but not that the time they form is valid. Only valid times can be considered peculiar:

- 00 ≤ XY < 24
- 00 ≤ ZT < 60

*Note*: you will receive full feedback for this problem.

# Input

The first line of the input will hold an integer **n <= 50**, describing the number of calls Xorin received.

The following **n** lines contain the time of one call each, in the format established above.

# Output

For each call, you should output on **n** separate lines, either "YES" - in case the respective call was made at a peculiar time - or "NO" - on the contrary. You should not output the quotation marks.

# Samples

Input | Output |
---|---|

5 12:34 00:00 00:01 10:10 91:19 | YES YES NO YES NO |

# The regular solution (Sergiu Puscas)

This is a straightforward implementation problem and does not require any algorithmic knowledge. For any given time, each of the criteria can be easily verified. Also, no integer manipulation is required, especially for the last two conditions, considering the small set of times that validate them:

- The only valid times that have consecutive digits are
**01:23**,**12:34**and**23:45**; - The only valid times that make up a number which is a power of two are
**10:24**and**20:48**(the next one,**40:96**, is already too large).

## C++ solution

1 #include <iostream> 2 using namespace std; 3 4 int t; 5 bool peculiar, valid; 6 char X, Y, Z, T, separator; 7 string fullTime, hour, minutes; 8 9 int main() { 10 cin>>t; 11 while(t--) { 12 cin>>X>>Y>>separator>>Z>>T; 13 fullTime.clear(); 14 fullTime.push_back(X); 15 fullTime.push_back(Y); 16 fullTime.push_back(Z); 17 fullTime.push_back(T); 18 19 hour.clear(); 20 hour.push_back(X); 21 hour.push_back(Y); 22 23 minutes.clear(); 24 minutes.push_back(Z); 25 minutes.push_back(T); 26 27 peculiar = false; 28 if(Z == '0' && T == '0') peculiar = true; 29 if(X == Z && Y == T) peculiar = true; 30 if(X == T && Y == Z) peculiar = true; 31 if(fullTime == "0123" || fullTime == "1234" || fullTime == "2345") peculiar = true; 32 if(fullTime == "1024" || fullTime == "2048") peculiar = true; 33 34 valid = true; 35 if(hour < "00" || hour >= "24") valid = false; 36 if(minutes < "00" || minutes >= "60") valid = false; 37 38 cout<<(valid && peculiar? "YES\n":"NO\n"); 39 } 40 41 return 0; 42 }

## Python solution

1 for _ in range(0, input()): 2 a, b = raw_input().split(':') 3 print ['NO', 'YES'][(b=='00' or a==b or a==b[::-1] or a+b in '0123 1234 2345 1024 2048'.split()) and a < '24' and b <= '60']

# A regex solution (Marius Gavrilescu)

This problem can also be solved using regular expressions, as seen in the following solution.1 #!/usr/bin/perl 2 use v5.14; 3 use warnings; 4 5 <>; 6 my $hour = qr/(?:[01]\d|2[0-3])/; # Matches a valid hour (00 - 23) 7 my $min = qr/[0-5]\d/; # Matches valid minutes (00 - 59) 8 my $time = qr/$hour:$min/; # Matches a valid time 9 my $exact = qr/\d\d:00/; # Matches exact hours (XY:00) 10 my $same = qr/(\d)(\d):(?:\1\2|\2\1)/; # Matches XY:XY and XY:YX 11 my $cons = qr/01:23|12:34|23:45/; # Matches consecutive digits 12 my $pow2 = qr/10:24|20:48/; # Matches a power of 2 13 14 my $peculiar = qr/(?:$exact|$same|$cons|$pow2)/; # Matches peculiar times 15 16 my $re = qr/(?=$time)$peculiar/; # Matches valid peculiar times 17 say m/$re/ ? 'YES' : 'NO' while <>;A typical way of writing the above:

1 #!/usr/bin/perl 2 use v5.14; 3 use warnings; 4 5 <>; 6 say /(?:[01]\d|2[0-3]):[0-5]\d/ && /:00|(\d)(\d):(?:\1\2|\2\1)|01:23|12:34|23:45|10:24|20:48/ ? 'YES' : 'NO' while <>;This solution can be golfed further if necessary.

1 <>;CORE::say/(?:[01]\d|2[0-3]):[0-5]\d/&&/:00|(\d)(\d):(?:\1\2|\2\1)|01:23|12:34|23:45|10:24|20:48/?YES:NO while<>;