Problem Statement

There are $N towns numbered 1,\ldots,N$ and $M roads numbered 1,\ldots,M$.
Road i connects towns A_i and B_i. When you use a road, your score changes as follows:

• when you move from town A_i to town B_i using road i, your score increases by C_i; when you move from town B_i to town A_i using road i, your score decreases by C_i.

Your score may become negative.
Answer the following Q questions.

• If you start traveling from town X_i with initial score 0, find the maximum possible score when you are at town Y_i.
  Here, if you cannot get from town X_i to town Y_i, print nan instead; if you can have as large a score as you want when you are at town Y_i, print inf instead.

Input

The input is given from Standard Input in the following format:
N M Q
A_1 B_1 C_1
$\vdots$
A_M B_M C_M
X_1 Y_1
$\vdots$
X_Q Y_Q

Output

Print Q lines as specified in the Problem Statement.
The i-th line should contain the answer to the i-th question.

Constraints

• $2\leq N \leq 10^5$
• $0\leq M \leq 10^5$
• $1\leq Q \leq 10^5$
• $1\leq A_i,B_i,X_i,Y_i \leq N$
• $0\leq C_i \leq 10^9$
• All values in the input are integers.

Sample Input 1

5 5 3
1 2 1
1 2 2
3 4 1
4 5 1
3 5 2
5 3
1 2
3 1

Sample Output 1

-2
inf
nan

For the first question, if you use road 5 to move from town 5 to town 3, you can have a score -2 when you are at town 3.
Since you cannot make the score larger, the answer is -2.
For the second question, you can have as large a score as you want when you are at town 2 if you travel as follows:
repeatedly "use road 2 to move from town 1 to town 2 and then use road 1 to move from town 2 to town 1" as many times as you want,
and finally use road 2 to move from town 1 to town 2.
For the third question, you cannot get from town 3 to town 1.

Sample Input 2

2 1 1
1 1 1
1 1

Sample Output 2

inf

The endpoints of a road may be the same, and so may the endpoints given in a question.

Sample Input 3

9 7 5
3 1 4
1 5 9
2 6 5
3 5 8
9 7 9
3 2 3
8 4 6
2 6
4 3
3 8
3 2
7 9

Sample Output 3

inf
nan
nan
inf
-9

见题面 Input 部分

见题面 Output 部分