Consider a set $A$ consisting of $n$ strings, each string of length $m$ and consisting of only the characters `0`, `1` or `*`. With a string, we can transform to get a binary string by replacing each character `*` in the string into a character `0` or `1`. Transform $n$ strings of set $A$ to obtain binary string set $B$ with the smallest value. Transform $n$ strings of set $A$ to obtain the set of binary strings $C$ with the largest value.
Requirement: Given $n$ strings, find a way to transform $n$ strings to get the set of binary strings $B$ with the smallest value and the set of binary strings $C$ with the largest value.
### Input
- The first line contains two positive integers $n,m$ $(m \le 100)$
- The following $n$ lines, each line consists of a string of length $m$ consisting of only the characters `0`,`1` or `*` describe $n$ strings of set $A$.
### Output
- The first line is an integer that is the cardinality of the set $B$; Next is $n$ binary string describing the way to transform each string in order to obtain the set $B$, the outputs are separated by exactly one space;
- The second line is an integer that is the value of the set $C$; Next is the binary string describing tje way to transform each string in order to obtain the set $C$, the outputs are separated by exactly one space.
### Example
Input:
```
4 3
***
01*
001
*1*
```
Output:
```
2 001 010 001 010
4 000 010 001 111
```
### Scoring:
There are $20$ test, each values $5.0$ points. Denote $s_B,s_C$ as the values of sets $B,C$ the students can find and the judge's answers are $w_B,w_C$,then the scoring for each test is:
$2.5$ $\times$ $min \\{1,(\dfrac{w_B}{s_B})^5)\\}$ + $2.5$ $\times$ $min \\{1,(\dfrac{s_C}{w_C})^5)\\}$
### Subtask
- Subtask 1 ($50 \\%$) : $n \le 10$
- Subtask 2 ($50 \\%$) : $n \le 1000$
