Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
2 3
1 3
1 2

Sample Output 1

3

All the conditions can be satisfied if the matches are scheduled for three days as follows:

Day 1: Player 1 vs Player 2

Day 2: Player 1 vs Player 3

Day 3: Player 2 vs Player 3

This is the minimum number of days required.

Sample Input 2

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

Sample Output 2

4

All the conditions can be satisfied if the matches are scheduled for four days as follows:

Day 1: Player 1 vs Player 2, Player 3 vs Player 4

Day 2: Player 1 vs Player 3

Day 3: Player 1 vs Player 4, Player 2 vs Player 3

Day 4: Player 2 vs Player 4

This is the minimum number of days required.

Sample Input 3

3
2 3
3 1
1 2

Sample Output 3

-1

Any scheduling of the matches violates some condition.

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

class DirectedGraph:
    def __init__(self, adj):
        self.n = len(adj)
        self.adj = adj
        self.is_asyclic = False
        self.max_path_len = None

    def topological_sort(self):
        indegree = [0] * self.n
        for i, vs in enumerate(self.adj):
            for dest in vs:
                indegree[dest] += 1
        zero_v = []
        for v, indeg in enumerate(indegree):
            if indeg == 0:
                zero_v.append(v)
        max_path_len = 1
        tp_sorted = []
        to_be_added = []
        while True:
            while zero_v:
                v = zero_v.pop()
                tp_sorted.append(v)
                for dest in self.adj[v]:
                    indegree[dest] -= 1
                    if indegree[dest] == 0:
                        to_be_added.append(dest)
            if len(to_be_added) > 0:
                zero_v += to_be_added
                to_be_added = []
                max_path_len += 1
            else:
                break
        if len(tp_sorted) == self.n:
            self.is_asyclic = True
            self.max_path_len = max_path_len
            return tp_sorted
        else:
            self.is_asyclic = False
            return None

if __name__ == "__main__":
    n = int(input())
    dic = {}
    itr = 0
    for i in range(n):
        for j in range(i+1, n):
            dic[i*n + j] = itr
            itr += 1
    edge = [[] for _ in range(n * (n-1) // 2)]
    for i in range(n):
        a = [int(item) - 1 for item in input().split()]
        for j1, j2 in zip(a, a[1:]):
            if i < j1:
                u = i * n + j1 
            else:
                u = j1 * n + i 
            if i < j2:
                v = i * n + j2 
            else:
                v = j2 * n + i 
            edge[dic[u]].append(dic[v])

    DG = DirectedGraph(edge)
    tps = DG.topological_sort()

    if DG.is_asyclic:
        print(DG.max_path_len)
    else:
        print(-1)