How to make an output file of n*n matrix,by taking n from the user, with the numbers generated in pairs?

Currently I have a pre-made 6X6 matrix in a text file like this:

2 6 3 1 0 4
4 2 7 7 2 8
4 7 3 2 5 1
7 6 5 1 1 0
8 4 6 0 0 6
1 3 1 8 3 8

and I made a code that is reading from a file i have made. However I want to have user make a grid for themselves (i.e. 3X3 or 10X10). Which then writes to a text file automatically like in similar fashion and then have that read-in instead. It is a basic memory match card game, so I need to have rand() which generates equal pair so the game can be over when every pair in the grid has been found. Thank you so much for your time!

/*Here are the snippets of my code*/

#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <ctime>
#include <vector>
#include <fstream>
#include <string>
#include <numeric>
#include <limits>

using namespace std;  

//global 2d vectors that are associated with the game
vector<vector<int> > game_grid; 
vector<vector<int> > hidden_grid;
vector <vector<int> > guessed;

void initialize_grid() {
ifstream input_file;
input_file.open("grid.txt");
int num;

if (input_file) {
    for (int i = 0; i < 6; ++i) {
        vector<int> row; // game grid
        vector<int> row2; // hidden grid
        vector<int> row3; // guessed grid
        for (int j = 0; j < 6; ++j) {
            if (input_file >> num)
                row.push_back(num);
            row2.push_back(-1);
            row3.push_back(0);
        }
        game_grid.push_back(row);
        hidden_grid.push_back(row2);
        guessed.push_back(row3);
    }
    cout << "Get is ready, Challenger!" << endl << endl;
}
else {
    cout << "Womp. File open failed!";
}
return;
}

void print_grid() {
cout << "Game  grid" << endl;
cout << " -------------------------" << endl;
for (int i = 0; i < 6; ++i) {
    cout << " | ";
    for (int j = 0; j < 6; ++j) {
        cout << game_grid[i][j] << " | ";
    }
    cout << endl << " -------------------------" << endl;
}
cout << endl;
}

void print_hidden_grid(int r1 = -1, int r2 = -1, int c1 = -1, int c2 = -1) {
cout << "Attempt:" << endl;
if (r1 != -1) {
    hidden_grid[r1][c1] = game_grid[r1][c1];
}
if (r2 != -1) {
    hidden_grid[r2][c2] = game_grid[r2][c2];
}
for (int i = 0; i < 6; ++i) {
    cout << " | ";
    for (int j = 0; j < 6; ++j) {
        if (hidden_grid[i][j] > -1)
            cout << hidden_grid[i][j] << " | ";
        else
            cout << "  | ";
    }
    cout << endl << " -------------------------" << endl;
}
cout << endl;

if (r1 != -1) {
    if (game_grid[r1][c1] == game_grid[r2][c2]) {
        guessed[r1][c1] = 1;
        guessed[r2][c2] = 1;
        cout << "You have a match!" << endl << endl;
    }
    else {
        hidden_grid[r1][c1] = -1;
        hidden_grid[r2][c2] = -1;
    }
}
cout << endl << endl;
}

void print_current_grid() {
cout << "Current Grid:" << endl;
cout << " -------------------------" << endl;
for (int i = 0; i < 6; ++i) {
    cout << " | ";
    for (int j = 0; j < 6; ++j) {
        if (hidden_grid[i][j] > -1)
            cout << hidden_grid[i][j] << " | ";
        else
            cout << "  | ";
    }
    cout << endl << " -------------------------" << endl;
}
cout << endl << endl;
}


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