Satellite Command Chain Power

A deep-space fleet is organized into command chains: every satellite has a unique id, an integer power rating, and a list of the ids of the satellites that report directly to it (its subordinate relays). A satellite's subordinates may themselves have subordinates, forming a hierarchy that can branch arbitrarily deep, and the fleet may contain several independent command chains (a forest, not necessarily a single tree).

Given a queried satellite id, compute the total power: the queried satellite's own power rating plus the power ratings of every satellite reachable by following the chain of command downward (its direct subordinates, their subordinates, and so on, transitively). Satellites outside that chain — including any commander above the queried satellite — must not be counted.

Input format

• Line 1: an integer n, the number of satellites.
• The next n lines each describe one satellite: id power k s_1 s_2 ... s_k, where id is that satellite's unique id, power is its integer power rating, k is the number of satellites reporting directly to it, followed by the k subordinate ids (omitted if k is 0).
• The last line contains a single integer queryId, the id of the satellite to query.

Output format

Print a single integer: the sum of power ratings for queryId and all satellites in its command chain.

Constraints

• 1 <= n <= 2*10^4
• The satellite ids are exactly the integers 1..n, each appearing exactly once as a satellite definition.
• -1000 <= power <= 1000
• Each satellite is listed as a direct subordinate of at most one other satellite, and the subordinate relationships contain no cycles (the structure is a forest).
• queryId is one of the ids 1..n.
• The sum of all k values equals n minus the number of root satellites (satellites with no commander).

4
1 5 2 2 3
2 3 0
3 1 1 4
4 7 0
1

16

4
1 5 2 2 3
2 3 0
3 1 1 4
4 7 0
2

3