CF149B.Martian Clock

Having stayed home alone, Petya decided to watch forbidden films on the Net in secret. "What ungentlemanly behavior!" — you can say that, of course, but don't be too harsh on the kid. In his country films about the Martians and other extraterrestrial civilizations are forbidden. It was very unfair to Petya as he adored adventure stories that featured lasers and robots.

Today Petya is watching a shocking blockbuster about the Martians called "R2:D2". What can "R2:D2" possibly mean? It might be the Martian time represented in the Martian numeral system. Petya knows that time on Mars is counted just like on the Earth (that is, there are 24 hours and each hour has 60 minutes). The time is written as "a:b", where the string a stands for the number of hours (from 0 to 23 inclusive), and string b stands for the number of minutes (from 0 to 59 inclusive). The only thing Petya doesn't know is in what numeral system the Martian time is written.

Your task is to print the radixes of all numeral system which can contain the time "a:b".

独自待在家中的佩蒂亚决定偷偷上网观看被禁止的电影。“这种行为真不绅士！”——你当然可以这么说，但请不要对这个孩子过于苛刻。在他所在的国家，关于火星人及其他地外文明的电影是被禁止的。这对佩蒂亚来说非常不公平，因为他特别喜爱那些以激光和机器人为题材的冒险故事。

今天佩蒂亚正在观看一部令人震惊的关于火星人的大片，片名为“R2:D2”。那么“R2:D2”究竟可能代表什么？它或许是用火星进制表示的火星时间。佩蒂亚知道，火星上的时间计法与地球相同（即一天有 24 小时，每小时有 60 分钟）。时间格式写作 _a_:_b_，其中字符串 _a_ 表示小时数（范围为 0 到 23，含端点），字符串 _b_ 表示分钟数（范围为 0 到 59，含端点）。佩蒂亚唯一不清楚的是：该时间究竟采用的是哪一种进制表示。

你的任务是：输出所有能够合法表示时间 _a_:_b_ 的进制（即基数）的值。

The first line contains a single string as "a:b" (without the quotes). There a is a non-empty string, consisting of numbers and uppercase Latin letters. String a shows the number of hours. String b is a non-empty string that consists of numbers and uppercase Latin letters. String b shows the number of minutes. The lengths of strings a and b are from 1 to 5 characters, inclusive. Please note that strings a and b can have leading zeroes that do not influence the result in any way (for example, string "008:1" in decimal notation denotes correctly written time).

We consider characters 0, 1, ..., 9 as denoting the corresponding digits of the number's representation in some numeral system, and characters A, B, ..., Z correspond to numbers 10, 11, ..., 35.

第一行包含一个形如 _a_:_b_（不含引号）的字符串。其中，_a_ 是一个非空字符串，由数字和大写拉丁字母组成，表示小时数；_b_ 也是一个非空字符串，由数字和大写拉丁字母组成，表示分钟数。字符串 _a_ 和 _b_ 的长度均为 1 到 5 个字符（含端点）。请注意，字符串 _a_ 和 _b_ 可能包含前导零，但这对结果没有任何影响（例如，在十进制下，字符串 "008:1" 表示一个合法的时间）。

我们约定：字符 0, 1, ..., 9 表示某进位制下数字表示中的对应数字；字符 A, B, ..., Z 分别对应数值 10, 11, ..., 35。

Print the radixes of the numeral systems that can represent the time "a:b" in the increasing order. Separate the numbers with spaces or line breaks. If there is no numeral system that can represent time "a:b", print the single integer 0. If there are infinitely many numeral systems that can represent the time "a:b", print the single integer -1.

Note that on Mars any positional numeral systems with positive radix strictly larger than one are possible.

按升序输出能够表示时间 “a:b” 的所有进制。用空格或换行分隔这些数字。如果不存在能够表示时间 “a:b” 的进制，则输出单个整数 0。如果存在无穷多个能够表示时间 “a:b” 的进制，则输出单个整数 $-1$。

注意：在火星上，允许使用任意基数严格大于 1 的正整数进制（即所有满足 $r > 1$ 且 $r \in \mathbb{Z}^+$ 的进制 $r$）。

Let's consider the first sample. String "11:20" can be perceived, for example, as time 4:6, represented in the ternary numeral system or as time 17:32 in hexadecimal system.

Let's consider the second sample test. String "2A:13" can't be perceived as correct time in any notation. For example, let's take the base-11 numeral notation. There the given string represents time 32:14 that isn't a correct time.

Let's consider the third sample. String "000B:00001" can be perceived as a correct time in the infinite number of numeral systems. If you need an example, you can take any numeral system with radix no less than 12.

我们来考虑第一个样例。字符串“11:20”可以被理解为例如三进制下的时间 4:6，或十六进制下的时间 17:32。

我们来考虑第二个样例测试。“2A:13”这个字符串在任何进制下都无法被理解为合法的时间。例如，考虑十一进制：该字符串在此进制下表示时间为 32:14，这不是一个合法的时间。

我们来考虑第三个样例。字符串“000B:00001”可以在无穷多个进制下被理解为合法的时间。若需举例，可任取一个基数不小于 12 的进制。