<|instruction|>
Solve the below problem. The solution should start with an abridged problem statement. Then key observations. Then full solution based on the observations. Then C++ and Python implementations with comments.

358. Median of Medians
Time limit per test: 0.25 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard



Vasya learned definition of median of three numbers. He says, "Median of three numbers is the number located in the middle when numbers are ordered in non-descending order". Subtle Pete gave him much more difficult task. Vasya has to find median of each of three triples and then find the median of three numbers he found. Please help Vasya with the task.

Input
The input file contains three lines. Each line contains three integers. Each number is not less than -1000 and is not greater than 1000.

Output
Print one number - median of three medians.

Example(s)
sample input
sample output
6 4 5 
7 9 8 
1 2 3
5

sample input
sample output
1 2 2 
4 3 2 
2 3 4
3

<|response|>
1. Abridged problem statement  
You are given a 3×3 grid of integers. For each of the three rows, compute the median (the middle value after sorting that row’s three numbers). Then, from those three medians, compute and output their median.

2. Key observations  
- With exactly three numbers, finding the median just means picking the second-smallest (i.e. sort and take index 1).  
- You perform that simple operation four times total: once per row (3 times) plus once on the collection of three medians.  
- Sorting or using a few comparisons on an array of size 3 is constant-time work, so this runs instantly for any valid input.

3. Full solution approach  
a. Read the input into a 3×3 array `a`.  
b. For each row `i` from 0 to 2:  
   i. Sort the three elements `a[i][0]`, `a[i][1]`, `a[i][2]`.  
   ii. Record the middle element (`a[i][1]`) as the row’s median.  
c. Collect these three medians into a small array or vector `m`.  
d. Sort `m` and output `m[1]`, the median of the medians.

4. C++ implementation
```cpp
#include <bits/stdc++.h>

using namespace std;

template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1, T2>& x) {
    return out << x.first << ' ' << x.second;
}

template<typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& x) {
    return in >> x.first >> x.second;
}

template<typename T>
istream& operator>>(istream& in, vector<T>& a) {
    for(auto& x: a) {
        in >> x;
    }
    return in;
};

template<typename T>
ostream& operator<<(ostream& out, const vector<T>& a) {
    for(auto x: a) {
        out << x << ' ';
    }
    return out;
};

vector<vector<int>> a;

void read() {
    a.assign(3, vector<int>(3));
    for(int i = 0; i < 3; i++) {
        cin >> a[i];
    }
}

void solve() {
    // Sort each of the three triples, take the middle element as that triple's
    // median, then sort those three medians and print the middle one.

    vector<int> medians;
    for(int i = 0; i < 3; i++) {
        sort(a[i].begin(), a[i].end());
        medians.push_back(a[i][1]);
    }

    sort(medians.begin(), medians.end());
    cout << medians[1] << '\n';
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int T = 1;
    // cin >> T;
    for(int test = 1; test <= T; test++) {
        read();
        // cout << "Case #" << test << ": ";
        solve();
    }

    return 0;
}
```

5. Python implementation with detailed comments  
```python
# Read the 3×3 grid from standard input
grid = [list(map(int, input().split())) for _ in range(3)]

# List to store the median of each row
medians = []

for row in grid:
    # Sort the row in non-decreasing order
    row.sort()
    # Take the middle element as the median
    medians.append(row[1])

# Now find the median of these three medians
medians.sort()
print(medians[1])
```