400470: GYM100187 J Deck Shuffling

The world famous scientist Innokentiy continues his innovative experiments with decks of cards. Now he has a deck of n cards and k shuffle machines to shuffle this deck. As we know, i-th shuffle machine is characterized by its own numbers p_i, 1, p_i, 2, ..., p_i, n such that if one puts n cards numbered in the order 1, 2, ..., n into the machine and presses the button on it, cards will be shuffled forming the deck p_i, 1, p_i, 2, ..., p_i, n where numbers p_i, 1, p_i, 2, ..., p_i, n are the same numbers of cards but rearranged in some order.

At the beginning of the experiment the cards in the deck are ordered as a₁, a₂, ..., a_n, i.e. the first position is occupied by the card with number a₁, the second position — by the card with number a₂, and so on. The scientist wants to transfer the card with number x to the first position. He can use all his shuffle machines as many times as he wants. You should determine if he can reach it.

In the first line the only positive integer n is written — the number of cards in the Innokentiy's deck.

The second line contains n distinct integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ n) — the initial order of cards in the deck.

The third line contains the only positive integer k — the number of shuffle machines Innokentiy has.

Each of the next k lines contains n distinct integers p_i, 1, p_i, 2, ..., p_i, n (1 ≤ p_i, j ≤ n) characterizing the corresponding shuffle machine.

The last line contains the only integer x (1 ≤ x ≤ n) — the number of card Innokentiy wants to transfer to the first position in the deck.

Numbers n and k satisfy the condition 1 ≤ n·k ≤ 200000.

Output «YES» if the scientist can transfer the card with number x to the first position in the deck, and «NO» otherwise.

4
4 3 2 1
2
1 2 4 3
2 3 1 4
1

YES

4
4 3 2 1
2
1 2 4 3
2 1 3 4
1

NO