405051: GYM101755 D Transfer Window

You play a football manager. There are n football players in the game, and k of them — a₁, a₂, ..., a_k — are currently playing in your team. You want players b₁, b₂, ..., b_k to play in your team. To achieve that, you can suggest other teams to exchange one of your players to their player.

For each ordered pair of distinct players (x, y) it is known whether or not a team controlled by AI would accept to exchange your player x to their player y. Determine whether it is possible to collect a team consisting of football players b₁, b₂, ..., b_k and if it is, output the order of exchanges to achieve it.

The first line contains two integers n and k (1 ≤ n ≤ 300, 1 ≤ k ≤ n) — the total number of football players in the game and the number of football players in your team.

The second line contains k distinct integers a_i (1 ≤ a_i ≤ n) — the players currently playing in your team.

The third line contains k distinct integers b_i (1 ≤ b_i ≤ n) — the players you want to see in your team.

Each of the next n lines contains n characters. Character in i-th line and j-th column equals «1», if the team controlled by AI would accept to exchange your player i to their player j, and «0», if it wouldn't. Characters on the main diagonal are equal to zero.

In the first line output «YES», if it's possible to make a team of players b₁, b₂,  ..., b_k, and «NO», if it's not.

In the case of the «YES» answer, in the second line output a single integer q (0 ≤ q ≤ n·n) — the number of exchanges, and then q lines — the sequence of exchanges. Each of these q lines must contain two distinct integers x_j and y_j (1 ≤ x_j ≤ n, 1 ≤ y_j ≤ n) — the number of player from your team you want to exchange and the number of player from another team you want to get for him. Please note that after j-th exchange player y_j becomes a player of your team and player x_j leaves your team.

If there are several sequences of exchanges leading to the desired result, output any of them. Also note that it's not required to minimize the number of exchanges, it's just enough if it doesn't exceed n·n.

5 2
1 2
4 5
00100
00100
00011
00000
00000

YES
4
1 3
3 4
2 3
3 5

3 2
1 2
2 3
000
001
010

NO