Curtains

문제

Benson the Rabbit is organizing a performance on his plane!

He has a stage with $nn$ sections numbered $11$ to $nn$ from left to right. He also has $mm$ curtains numbered from $11$ to $mm$.

Each of these $mm$ curtains can be lowered. Lowering curtain $ii$ covers sections $l[i]l[i]$ to $r[i]r[i]$. A curtain configuration is a set of lowered curtains. Given a curtain configuration, a section $xx$ (1 ≤ x ≤ n) is covered if and only if there exists a lowered curtain $ii$ such that l[i] ≤ x ≤ r[i].

Benson wants to give a total of $qq$ performances, numbered from $11$ to $qq$. For each performance $jj$, Benson requires a curtain configuration such that the sections $s[j]s[j]$ to $e[j]e[j]$ are covered and nothing else is covered. More formally, for each 1 ≤ x ≤ n,

• If s[j] ≤ x ≤ e[j], section $xx$ is covered.
• Otherwise, section $xx$ is not covered.

For each of these $qq$ performances, help Benson to determine if there exists a curtain configuration satisfying his requirements.

입력

The first line of input will contain $33$ spaced integers $nn$, $mm$ and $qq$, representing the number of sections, curtains and performances respectively.

The next $mm$ lines of input will contain $22$ spaced integers each. The $ii$-th of these lines will contain $l[i]l[i]$ and $r[i]r[i]$ respectively, describing the range of sections that curtain $ii$ can cover.

The next $qq$ lines of input will contain $22$ spaced integers each. The $jj$-th of these lines will contain $s[j]s[j]$ and $e[j]e[j]$ respectively, describing the range of sections that need to be covered for performance $jj$.

출력

Output $qq$ lines, the $jj$-th of which should contain YES if it is possible to cover the required sections for the $jj$-th performance using the curtains, and NO otherwise.

6 2 3
1 2
3 4
1 3
1 4
1 5

NO
YES
NO

10 10 10
6 9
6 7
1 6
10 10
5 9
3 9
2 10
5 7
9 10
5 10
7 8
4 7
1 6
2 7
3 9
7 7
2 9
4 9
6 6
5 7

NO
NO
YES
NO
YES
NO
NO
NO
NO
YES