A release tool publishes a proposed build order: a permutation of all n modules. A directed edge u v means module u must be built before module v. The proposed order is valid if and only if, for every edge u v, module u appears earlier than module v in the order. Decide whether the proposed order is valid.

Input format

Line 1: two integers n and m — the number of nodes (labeled 0 through n-1) and the number of directed edges. Each of the next m lines: two integers u v, a directed edge from u to v (read as: u must come before v). The final line: n space-separated integers, a permutation of 0..n-1 giving the proposed build order (first built to last built).

Output format

Print YES if the proposed order satisfies every edge, otherwise NO.

Constraints

• 1 <= n <= 100000
• 0 <= m <= 200000
• 0 <= u, v <= n-1 (a self-loop u u can never be satisfied)
• The final line is guaranteed to be a permutation of 0..n-1.

3 2
0 1
1 2
0 1 2

YES

3 2
0 1
1 2
1 0 2

NO