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 $n$ words in his head, and there are $m$ connections between some words. The connection between words $x$ and $y$, with time $t$, means that if Rafael remembers the word $x$ or hears it, after $t$ milliseconds he will remember the word $y$.

Novak and Rafael will play $q$ rounds. In each round, Novak wants to know: if he says the word $a$, after how many milliseconds will Rafael remember the word $b$ for the first time? The rounds are independent.

Input Specification

The first line contains integers $n$ $(2\le n\le 1000)$ and $m$ $(1\le m\le 1000)$, the number of words and the number of connections.

Each of the following $m$ lines contains two different words $x_i$ and $y_i$, and an integer $t_i$ $(1\le t_i\le {10}^9)$, that describe a connection. The words consist of at most $20$ 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 $q$ $(1\le q\le 1000)$, the number of rounds.

Each of the following $q$ lines contains two different words $a_i$ and $b_i$, the word that Novak will say and the word that Rafael needs to remember in the $i^{\text{th}}$ round. Both words appear in Rafael's database.

Output Specification

Output $q$ lines. In the $i^{\text{th}}$ line output the time for the $i^{\text{th}}$ round in milliseconds, or Roger if Rafael will never remember the word.

Constraints

Subtask	Points	Constraints
1	20	$2\le n\le 10$
2	20	$2\le n\le 100$
3	30	No additional constraints.

Sample Input 1

3 2
novak goat 1
goat simulator 3
2
novak simulator
simulator goat

Sample Output 1

4
Roger

Explanation for Sample Output 1

In the first round, Novak will say the word novak. After $1$ millisecond, Rafael will remember the word goat, and after $3$ 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

9
11

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