League

N players will participate in a tennis tournament. We will call them Player 1, Player 2, \ldots, Player N.

The tournament is round-robin format, and there will be N(N-1)/2 matches in total. Is it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.

• Each player plays at most one matches in a day.
• Each player i (1 \leq i \leq N) plays one match against Player A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} in this order.

Constraints

• 3 \leq N \leq 1000
• 1 \leq A_{i, j} \leq N
• A_{i, j} \neq i
• A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} are all different.

Input

Input is given from Standard Input in the following format:

N A_{1, 1} A_{1, 2} \ldots A_{1, N-1} A_{2, 1} A_{2, 2} \ldots A_{2, N-1} : A_{N, 1} A_{N, 2} \ldots A_{N, N-1}

Output

If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.

Examples

Input

3 2 3 1 3 1 2

Output

3

Input

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

Output

4

Input

3 2 3 3 1 1 2

Output

-1

inputFormat

Input

Input is given from Standard Input in the following format:

N A_{1, 1} A_{1, 2} \ldots A_{1, N-1} A_{2, 1} A_{2, 2} \ldots A_{2, N-1} : A_{N, 1} A_{N, 2} \ldots A_{N, N-1}

outputFormat

Output

If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.

Examples

Input

3 2 3 1 3 1 2

Output

3

Input

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

Output

4

Input

3 2 3 3 1 1 2

Output

-1

样例

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

4