Problem:
Score : 700 points

Problem Statement

Takahashi is hosting an sports meet.
There are N people who will participate. These people are conveniently numbered 1 through N.
Also, there are M options of sports for this event. These sports are numbered 1 through M.
Among these options, Takahashi will select one or more sports (possibly all) to be played in the event.

Takahashi knows that Person i's j-th favorite sport is Sport A_{ij}.
Each person will only participate in his/her most favorite sport among the ones that are actually played in the event, and will not participate in the other sports.

Takahashi is worried that one of the sports will attract too many people.
Therefore, he would like to carefully select sports to be played so that the number of the participants in the sport with the largest number of participants is minimized.
Find the minimum possible number of the participants in the sport with the largest number of participants.

Constraints

1 \leq N \leq 300

1 \leq M \leq 300

A_{i1} , A_{i2} , ... , A_{iM} is a permutation of the integers from 1 to M.

Input

Input is given from Standard Input in the following format:

N M
A_{11} A_{12} ... A_{1M}
A_{21} A_{22} ... A_{2M}
:
A_{N1} A_{N2} ... A_{NM}

Output

Print the minimum possible number of the participants in the sport with the largest number of participants.

Sample Input 1

4 5
5 1 3 4 2
2 5 3 1 4
2 3 1 4 5
2 5 4 3 1

Sample Output 1

2

Assume that Sports 1, 3 and 4 are selected to be played. In this case, Person 1 will participate in Sport 1, Person 2 in Sport 3, Person 3 in Sport 3 and Person 4 in Sport 4.
Here, the sport with the largest number of participants is Sport 3, with two participants.
There is no way to reduce the number of participants in the sport with the largest number of participants to 1. Therefore, the answer is 2.

Sample Input 2

3 3
2 1 3
2 1 3
2 1 3

Sample Output 2

3

Since all the people have the same taste in sports, there will be a sport with three participants, no matter what sports are selected.
Therefore, the answer is 3.

Solution in Python (3.8.2) (judge verdict: Accepted)

# chokudaiブログの典型力の話を意識しつつ考えたら思いついた!

# 「ある集合の部分集合の中で、〜〜〜の値が最小になるものを求めよ」のパターン
# 愚直にやると2^Nを調べねばならず無理。
# したがって「一部を調べればよい」に帰着するのが多いだろう。
# 何らかの形でソートしておいて、空集合から1つずつ付け加えるとか。全体集合から1つずつ取り去るとか。

# 今回は全体集合から1つずつ取り去るのを考えるとできる。
# 全体集合である競技m0が最多の人数p0人を集めたとする。
# すると、全ての部分集合のうち「m0を含む集合」を考えると、競技m0は必ずp0人以上集まるので解もp0以上。
# ここで「m0を含む集合」について一気に計算できていることに注意! 一撃で多数の集合について計算が終わる。
# 次に全体集合からm0を取り去ったものを考える。
# ここである競技m1が最多の人数p1人を集めたとする。すると……以下同様。
# なお複数種目の競技が同率1位になった場合は全て一度に取り除いて良い。
# これで空集合までやって、最大が最小のものを出力すればOK! 

n, m = list(map(int, input().split()))
preference = [list(map(lambda x: int(x) - 1, input().split())) for _ in range(n)] # 1-index → 0-index

ans = n
held_sports = set(range(m))

while held_sports:
    # 各競技に参加する人数を求める
    parti = [0] * m
    for pref in preference:
        for s in range(m):
            if pref[s] in held_sports:
                parti[pref[s]] += 1
                break
    
    temp = max(parti)
    ans = min(ans, temp)
    # 集合から最大人数を取った要素を除外
    for idx, par in enumerate(parti):
        if par == temp:
            held_sports.remove(idx)

print(ans)