#define _CRT_SECURE_NO_WARNINGS

#include <iostream>


bool is_that_complete(int **matrix, int v)
{
    for (int i = 0;i<v; i++)
    {
        for (int j = 0; j < v; j++)
        {
            if (i == j) continue;
            if (matrix[i][j] == 0) return false;
        }
    }

    return true;
}

bool is_that_cycle(int **matrix, int v)
{
    int licznik = 0;

    int *odwiedzone = new int[v];
    for (int i = 0; i < v; i++)
    {
        odwiedzone[i] = -1;

    }

    int s = 0;
    for (int i = 0; i < v; i++)
    {
        for (int j = 0; j < v; j++)
        {
            if (matrix[s][j] == 1 && odwiedzone[j] == -1)
            {
                odwiedzone[j] = 1;

                matrix[s][j] = 0;
                matrix[j][s] = 0;
                licznik++;
                s = j;
                j = 0;

                break;

            }
        }
    }

    bool tr = true;

    for (int i = 0; i <v; i++)
    {
        if (odwiedzone[i] == -1)
        {
            tr = false;
            break;
        }
    }

    delete[] odwiedzone;
    if (licznik == v && s == 0 && tr == true) return true;
    else return false;
}

int main()
{
    int n, v;
    scanf("%d", &n);

    for (int k = 0; k < n; k++)
    {
        //start of allocation

        scanf("%d", &v);

        int **matrix = new int*[v];

        for (int i = 0; i < v; i++)
        {
            matrix[i] = new int[v];
        }
        int *colors = new int[v];

        for (int i = 0; i < v; i++)
        {
            colors[i] = 0;
        }

        char *mat = new char[v*v + 1];

        scanf("%s", mat);

        for (int i = 0; i < v*v; i++)
        {
            if (mat[i] == '1') matrix[i / v][i%v] = 1;
            else matrix[i / v][i%v] = 0;
        }

        //end of allocation

        //calculations start

        //Is it complete graph?
        if (is_that_complete(matrix, v))
        {
            printf("True\n");
        }
        //Is it an odd cycle?
        else if (v % 2 == 1)
        {
            if (is_that_cycle(matrix, v))
            {
                printf("True\n");
            }
            else printf("False\n");
        }
        else printf("False\n");


        //calculations end

        //deallocation start

        for (int i = 0; i < v; i++)
        {
            delete[] matrix[i];
        }

        delete[] matrix;
        delete[] mat;

        //deallocation end
    }


}