Backtracking task got TRAGIC

I was solving this task:

Let us consider the problem of calculating the number of paths in an n × n grid from the upper-left corner to the lower-right corner such that the path visits each square exactly once.

And for some reason my code isn't working properly, it should output 2 when the grid is 3 by 3, but for some reason it doesn't get to the last square and just stops with the output of 1.

#include <iostream>
#include <vector>
using namespace std;

long ans = 0;
const int n = 3;
int num = 3 * 3;
bool grid[n][n];

void search(int x, int y, int checked) {
    grid[x][y] = true;
    cout << "Searching in " << x << " " << y << " in " << checked << "\n";

    if (checked == num) {
        cout << "in IF!\n";
        if (x == n - 1 && y == n - 1){
            ans++;
            cout << "ans++!\n";
        }
        return;
    }   
    else {
        //Left
        if (x > 0 && !grid[x - 1][y]) {
            checked++;
            search(x - 1, y, checked);
            checked--;
        }

        //Right
        if (x < n - 1 && !grid[x + 1][y]) {
            checked++;
            search(x + 1, y, checked);
            checked--;
        }

        //Up
        if (y != 0 && !grid[x][y - 1]) {
            checked++;
            search(x, y - 1, checked);
            checked--;
        }

        //Down
        if (y != n - 1 && !grid[x][y + 1]) {
            checked++;
            search(x, y + 1, checked);
            checked--;
        }
    }
    grid[x][y] = false;
    return;

}

int main() {
    search(0, 0, 1);
    cout << ans;
    return 0;
}

Tried everything and no results.

Be careful when creating multiple paths through your code that they all perform all of the required actions.

When you find the end square you return without resetting grid[x][y] to false. Removing this return makes your code generate your expected result: https://godbolt.org/z/873jhG668

It's probably overkill in this scenario but in general you can avoid this in C++ with the RAII pattern.