Novak and Rafael are playing a simplified version of the game Alias. Novak needs to make Rafael guess a word without saying it. Rafael has a database of words in his head, and there are connections between some words. The connection between words and , with time , means that if Rafael remembers the word or hears it, after milliseconds he will remember the word .
Novak and Rafael will play rounds. In each round, Novak wants to know: if he says the word , after how many milliseconds will Rafael remember the word for the first time? The rounds are independent.
The first line contains integers and , the number of words and the number of connections.
Each of the following lines contains two different words and , and an integer , that describe a connection. The words consist of at most lowercase letters. All words from Rafael's database will appear at least once. It is possible that there are multiple connections between some pairs of words.
The following line contains an integer , the number of rounds.
Each of the following lines contains two different words and , the word that Novak will say and the word that Rafael needs to remember in the round. Both words appear in Rafael's database.
Output lines. In the line output the time for the round in milliseconds, or
Roger if Rafael will never remember the word.
|3||30||No additional constraints.|
Sample Input 1
3 2 novak goat 1 goat simulator 3 2 novak simulator simulator goat
Sample Output 1
Explanation for Sample Output 1
In the first round, Novak will say the word
novak. After millisecond, Rafael will remember the word
goat, and after more milliseconds the required word
simulator. In the second round, Novak will say the word
simulator, but Rafael won't remember any other words.
Sample Input 2
3 3 kile legend 4 legend beer 5 beer kile 6 2 kile beer legend kile
Sample Output 2
Sample Input 3
4 5 rafael me 5 me ow 6 ow ausopenfinal 2012 ausopenfinal me 2 rafael ausopenfinal 2 3 rafael me me rafael ow me
Sample Output 3
4 Roger 2014