human
Give me a Python program to find the value α=min\\{a_1, a_2, given the following:
Vlad has n friends, for each of whom he wants to buy one gift for the New Year.

There are m shops in the city, in each of which he can buy a gift for any of his friends. If the j-th friend (1 ≤ j ≤ n) receives a gift bought in the shop with the number i (1 ≤ i ≤ m), then the friend receives p_{ij} units of joy. The rectangular table p_{ij} is given in the input.

Vlad has time to visit at most n-1 shops (where n is the number of friends). He chooses which shops he will visit and for which friends he will buy gifts in each of them.

Let the j-th friend receive a_j units of joy from Vlad's gift. Let's find the value α=min\\{a_1, a_2, ..., a_n\}. Vlad's goal is to buy gifts so that the value of α is as large as possible. In other words, Vlad wants to maximize the minimum of the joys of his friends.

For example, let m = 2, n = 2. Let the joy from the gifts that we can buy in the first shop: p_{11} = 1, p_{12}=2, in the second shop: p_{21} = 3, p_{22}=4.

Then it is enough for Vlad to go only to the second shop and buy a gift for the first friend, bringing joy 3, and for the second — bringing joy 4. In this case, the value α will be equal to min\{3, 4\} = 3

Help Vlad choose gifts for his friends so that the value of α is as high as possible. Please note that each friend must receive one gift. Vlad can visit at most n-1 shops (where n is the number of friends). In the shop, he can buy any number of gifts.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input.

An empty line is written before each test case. Then there is a line containing integers m and n (2 ≤ n, 2 ≤ n ⋅ m ≤ 10^5) separated by a space — the number of shops and the number of friends, where n ⋅ m is the product of n and m.

Then m lines follow, each containing n numbers. The number in the i-th row of the j-th column p_{ij} (1 ≤ p_{ij} ≤ 10^9) is the joy of the product intended for friend number j in shop number i.

It is guaranteed that the sum of the values n ⋅ m over all test cases in...
Using python3 can you solve the prior task?
assistant
#Here is Python program to find the value α=min\\{a_1, a_2, .

import sys
import io, os
input = sys.stdin.buffer.readline
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

from collections import Counter, defaultdict

t = int(input())
for _ in range(t):
    blank = input()
    m, n = map(int, input().split())
    P = [list(map(int, input().split())) for i in range(m)]

    def is_ok(x):
        C = Counter()
        D = defaultdict(lambda: [])
        for i in range(n):
            for j in range(m):
                if P[j][i] >= x:
                    C[j] += 1
                    D[i].append(j)
            if not D[i]:
                return False
        #print(x)
        #print(C)
        #print(D)
        for i in range(n):
            for j in D[i]:
                if C[j] >= 2:
                    return True
        return False

    ok = 0
    ng = 10**9+50
    while ok+1 < ng:
        c = (ng+ok)//2
        if is_ok(c):
            ok = c
        else:
            ng = c
    print(ok)