## IFCHAIN - If Chain

Consider the following code:

if (a)

if (b)

if (c)

foo();

where *a,b *and *c* are boolean variables. If we run this code in C++, the function *foo()* is called if and only if all three variables are true. However, recently a new language - C-- - is being developed. In this language, when an *if()* evaluates to false, only the statement directly following it is not executed; for example, if *a* was false, the program would jump from *if(a)* to *if(c)*.

Using this convention, there are 5 different possible assignments of truth values to the variables *a*,*b*,*c* which end up calling *foo()*. Considering *a*,*b*,*c* as three bits in that order, they are 111, 101, 100, 011 and 001.

Given **n** boolean variables within a chain of **m** *if()*'s, where the variables within one *if()* are separated using **logical or**, count the number of ways to assign truth values to them which end up calling the function *foo()* (the call to *foo()* is after the last *if()*).

### Input

The first line of the input is the number of test cases **1 ≤ ****T ≤ 30**. **T **test cases follow.

The first line of each test case contains two nonnegative integers **n ≤ 10 ^{5}** - the number of boolean variables (they are numbered

**1**through

**n**) - and

**m ≤ 10**- the number of

^{5}*if()*'s.

**m**lines follow, the

**i**-th line describing the

**i**-th

*if()*. The first integer in each line contains a positive integer

**k**- the number of variables in the

_{i}**i**-th

*if()*(implicitly separated by the

**logical or**operator) - followed by

**k**positive integers in the range

_{i}**[1,n]**: the variables in the

**i**-th

*if()*. Not all variables need necessarily appear within the

*if()*chain, and the variables within one

*if()*need not be distinct.

The sum of **k _{i}** within a test case will not exceed

**5*10**. Additionally, the sum of

^{5}**n**,

**m**and

**k**within a single input file will not exceed

_{i}_{ }**2*10**

^{6}.**The input is quite large - make sure to read it efficiently.**

### Output

For each case, output the string "Case **x**:** y**" in a single line, where **x** is the number of the test case, starting from 1, and **y **is the number of ways of assigning truth values to the **n** boolean variables (out of **2 ^{n}**), which when run in C-- end up calling

*foo()*, modulo

**10**.

^{9}+9### Example

Input:2 3 3 1 1 1 2 1 3 5 3 2 1 2 3 1 3 5 2 2 4Output:Case 1: 5 Case 2: 24

Added by: | Hodobox |

Date: | 2017-05-22 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All |

Resource: | own problem |