Missile war

There are two countries \(A\) and \(B\) at war. Country \(A\) plans to attack \(t\) number of targets and country \(B\) wants to defend them.

\(A\) has \(n\) missile systems. Each missile system has a set of predifined targets and will attack all targets in that set.

\(B\) has \(m\) defence systems. Each defence system has a set of predifined targets and a defence capacity \(c\). A single defence system can choose to defend \(r\) targets in it’s set such that \(r \leq c\).

Your task is to find out the maximum amount of succesful defence operations that can be carried out by \(B\).

There can be multiple defence operations on a single target.

Input Format

• First line contains three space seperated integers \(n\) \(m\) \(t\)
• next \(n\) lines contains attack range of \(i^{th}\) (\(1 \leq i \leq n\)) missile system,

  • integer $$

    r_i

    \(followed by\)

    r_i

    \(space seperated integers\)r_i\(. (\)r_i\(are the targets of the Missile system\)i$$)

• next \(m\) lines contains defence range of \(i^{th}\) (\(1 \leq i \leq m\)) missile system,

  • integer $$

    r_i

    \(followed by\)

    r_i

    \(space seperated integers\)r_i\(. (\)r_i\(are the targets of the defence system\)i$$)

• next line contains \(m\) space seperated integers (Capacity of each defence system)

Output Format

• Single Integer - maximum amount of succesful defence operations

Constraints

Constraints:

• \[1 \leq n,m,t \leq 10^3\]
• \[0 \leq c_i \leq 10^3\]

• $ 0 \leq

  r_i

  \leq 10^3$

Sample Input 0

2 2 3
1 1
2 2 3
2 1 2
1 3
1 2

Sample Output 0

2