The programming language Ada has integer constants that look like this: 123, 8#123#, 16#abc#. These constants represent the integers 123, 83 (123 base 8) and 2739 (abc base 16). More precisely, an integer may be a decimal inte- ger given as a sequence of one or more digits less than 10, or it may be an integer to some specific base, given as the base followed by a sequence of one or more digits less than the base enclosed by # symbols. Lower case letters from a through f are used as the digits representing 10 through 15. In Ada, the base, if specified, must be a sequence of decimal digits. For this problem, however, the base may be of any form described above so long as it represents an integer between 2 and 16 inclusive. Input The first line of input contains a positive integer n. n lines follow. Output For each line of input, output a line ‘yes’ if it is a valid integer constant according to the above rules; otherwise output a line containing ‘no’. Input lines contain no spaces and are between 1 and 80 characters in length. Sample Input 5 2#101# 2#101##123# 17#abc# 16#123456789abcdef# 16#123456789abcdef#123456789abcdef# Sample Output yes yes no yes no