Problem:
Score: 400 points

Problem Statement

In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east.
A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).
Takahashi the king is interested in the following Q matters:

The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.

Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.

Constraints

N is an integer between 1 and 500 (inclusive).

M is an integer between 1 and 200 \ 000 (inclusive).

Q is an integer between 1 and 100 \ 000 (inclusive).

1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)

1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q

Output

Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.

Sample Input 1

2 3 1
1 1
1 2
2 2
1 2

Sample Output 1

3

As all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.

Sample Input 2

10 3 2
1 5
2 8
7 10
1 7
3 10

Sample Output 2

1
1

The first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.
The second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.

Sample Input 3

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

Sample Output 3

7
9
10
6
8
9
6
7
8
10

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

N,M,Q=gets.chomp.split(" ").map { |e| e.to_i  }

LR=Array.new(M)
PQ=Array.new(Q)
dpup = Array.new(N+1,-1)
dpdown = Array.new(N+1,-1)
ans = Array.new(Q+1,-1)


M.times do |i|
  l,r=gets.chomp.split(" ").map { |e| e.to_i  }
  LR[i] = {'l' => l,'r' => r}
end

Q.times do |i|
  p,q=gets.chomp.split(" ").map { |e| e.to_i  }
  PQ[i] = {'p' => p, 'q' => q}
end

def in(lr,pq)
  if pq["p"] <= lr["l"] && lr["r"] <= pq["q"]
    return true
  end
end


Q.times do |i|
  l=0
  r=0


  if dpdown[PQ[i]["p"]] != -1
    l = dpdown[PQ[i]["p"]]
  else
    M.times do |j|
      if PQ[i]["p"] <= LR[j]["l"]
        l += 1
      end
    end
    dpdown[PQ[i]["p"]] = l
  end

  if dpup[PQ[i]["q"]] != -1
    r = dpup[PQ[i]["q"]]
  else
    M.times do |k|
      if LR[k]["r"] <= PQ[i]["q"]
        r +=1
      end
    end
    dpup[PQ[i]["q"]] = r
  end

ans[i+1] = [l,r].min

end

puts ans.drop(1)