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G - Elevators

Score : $600$ points

Problem Statement

There is a complex composed of $N$ $10^9$-story skyscrapers. The skyscrapers are numbered $1$ to $N$, and the floors are numbered $1$ to $10^9$.

From any floor of any skyscraper, one can use a skybridge to get to the same floor of any other skyscraper in one minute.

Additionally, there are $M$ elevators. The $i$-th elevator runs between Floor $B_i$ and Floor $C_i$ of Skyscraper $A_i$. With this elevator, one can get from Floor $x$ to Floor $y$ of Skyscraper $A_i$ in $|x-y|$ minutes, for every pair of integers $x,y$ such that $B_i \le x,y \le C_i$.

Answer the following $Q$ queries.

• Determine whether it is possible to get from Floor $Y_i$ of Skyscraper $X_i$ to Floor $W_i$ of Skyscraper $Z_i$, and find the shortest time needed to get there if it is possible.

Constraints

• $1 \le N,M,Q \le 2 \times 10^5$
• $1 \le A_i \le N$
• $1 \le B_i < C_i \le 10^9$
• $1 \le X_i,Z_i \le N$
• $1 \le Y_i,W_i \le 10^9$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$N$ $M$ $Q$

$A_1$ $B_1$ $C_1$

$A_2$ $B_2$ $C_2$

$\vdots$

$A_M$ $B_M$ $C_M$

$\mathrm{query}_1$

$\mathrm{query}_2$

$\vdots$

$\mathrm{query}_Q$

Each query is in the following format:

``` $X_i$ $Y_i$ $Z_i$ $W_i$ ```

Output

Print $Q$ lines. The $i$-th line should contain -1 if, for $\mathrm{query}_i$, the destination is unreachable; otherwise, it should contain the minimum number of minutes needed to get there.

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3 4 3
1 2 10
2 3 7
3 9 14
3 1 3
1 3 3 14
3 1 2 7
1 100 1 101

12
7
-1

For the $1$-st query, you can get to the destination in $12$ minutes as follows.

• Use Elevator $1$ to get from Floor $3$ to Floor $9$ of Skyscraper $1$, in $6$ minutes.
• Use the skybridge on Floor $9$ to get from Skyscraper $1$ to Skyscraper $3$, in $1$ minute.
• Use Elevator $3$ to get from Floor $9$ to Floor $14$ of Skyscraper $3$, in $5$ minutes.

For the $3$-rd query, the destination is unreachable, so -1 should be printed.

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1 1 1
1 1 2
1 1 1 2

1