Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

Output

Here's a C program that counts the total number of unholy 8x8 binary matrices: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices(int level, int mat[SIZE][SIZE]) {
    int count = 0;

    if (level == SIZE * SIZE) {
        if (is_unholy(mat)) {
            count = 1;
        }
        return count;
    }

    int i = level / SIZE;
    int j = level % SIZE;

    mat[i][j] = 0;
    count += count_unholy_matrices(level + 1, mat);

    mat[i][j] = 1;
    count += count_unholy_matrices(level + 1, mat);

    return count;
}

int main() {
    int mat[SIZE][SIZE] = {{0}};
    int total_count = count_unholy_matrices(0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", total_count);
    return 0;
}
This program uses recursion to generate and count all possible 8x8 binary matrices. The `is_unholy()` function checks whether a given matrix is unholy or not. The `count_unholy_matrices()` function recursively generates matrices and counts the unholy ones. The main function initializes an empty matrix and calls `count_unholy_matrices()` to get the total count.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices(int level, int mat[SIZE][SIZE]) {
    int count = 0;

    if (level == SIZE * SIZE) {
        if (is_unholy(mat)) {
            count = 1;
        }
        return count;
    }

    int i = level / SIZE;
    int j = level % SIZE;

    mat[i][j] = 0;
    count += count_unholy_matrices(level + 1, mat);

    mat[i][j] = 1;
    count += count_unholy_matrices(level + 1, mat);

    return count;
}

int main() {
    int mat[SIZE][SIZE] = {{0}};
    int total_count = count_unholy_matrices(0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", total_count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices(int level, int mat[SIZE][SIZE]) {
    int count = 0;

    if (level == SIZE * SIZE) {
        if (is_unholy(mat)) {
            count = 1;
        }
        return count;
    }

    int i = level / SIZE;
    int j = level % SIZE;

    mat[i][j] = 0;
    count += count_unholy_matrices(level + 1, mat);

    mat[i][j] = 1;
    count += count_unholy_matrices(level + 1, mat);

    return count;
}

int main() {
    int mat[SIZE][SIZE] = {{0}};
    int total_count = count_unholy_matrices(0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", total_count);
    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

Output

Here's a C program that counts the total number of unholy 8x8 binary matrices: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices() {
    int total = 0;
    int mat[SIZE][SIZE];

    // Iterate through all 2^64 possible binary matrices
    for (int i = 0; i < (1 << (SIZE * SIZE)); i++) {
        // Convert integer to binary matrix representation
        for (int r = 0; r < SIZE; r++) {
            for (int c = 0; c < SIZE; c++) {
                mat[r][c] = (i & (1 << (r * SIZE + c))) ? 1 : 0);
            }
        }

        if (is_unholy(mat)) {
            total++;
        }
    }

    return total;
}

int main() {
    int total_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", total_unholy);

    return 0;
}
This program defines a helper function `is_unholy()` to determine whether a given 8x8 binary matrix is unholy. The `count_unholy_matrices()` function iterates through all possible 2^64 binary matrices and checks if they are unholy using the `is_unholy()` function. The total count of unholy matrices is then printed in the `main()` function.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices() {
    int total = 0;
    int mat[SIZE][SIZE];

    // Iterate through all 2^64 possible binary matrices
    for (int i = 0; i < (1 << (SIZE * SIZE)); i++) {
        // Convert integer to binary matrix representation
        for (int r = 0; r < SIZE; r++) {
            for (int c = 0; c < SIZE; c++) {
                mat[r][c] = (i & (1 << (r * SIZE + c))) ? 1 : 0);
            }
        }

        if (is_unholy(mat)) {
            total++;
        }
    }

    return total;
}

int main() {
    int total_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", total_unholy);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int mat[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (i == SIZE - 1 || mat[i + 1][j] == 0) &&
                    (j == SIZE - 1 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int count_unholy_matrices() {
    int total = 0;
    int mat[SIZE][SIZE];

    // Iterate through all 2^64 possible binary matrices
    for (int i = 0; i < (1 << (SIZE * SIZE)); i++) {
        // Convert integer to binary matrix representation
        for (int r = 0; r < SIZE; r++) {
            for (int c = 0; c < SIZE; c++) {
                mat[r][c] = (i & (1 << (r * SIZE + c))) ? 1 : 0);
            }
        }

        if (is_unholy(mat)) {
            total++;
        }
    }

    return total;
}

int main() {
    int total_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", total_unholy);

    return 0;
}
And got the output: main.c: In function 'count_unholy_matrices': main.c:27:28: warning: left shift count >= width of type [-Wshift-count-overflow] 27 | for (int i = 0; i < (1 << (SIZE * SIZE)); i++) { | ^~ main.c:31:64: error: expected ';' before ')' token 31 | mat[r][c] = (i & (1 << (r * SIZE + c))) ? 1 : 0); | ^ | ; main.c:31:64: error: expected statement before ')' token main.sh: line 2: ./a.out: No such file or directory

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

Output

Here is a C program that counts the total number of unholy 8x8 matrices. This program uses a recursive function to generate all possible 8x8 binary matrices and checks each one to see if it is unholy. 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0;

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_isolated(int i, int j, int mat[8][8]) {
    if (i > 0 && mat[i - 1][j] == 1)
        return 0;
    if (i < 7 && mat[i + 1][j] == 1)
        return 0;
    if (j > 0 && mat[i][j - 1] == 1)
        return 0;
    if (j < 7 && mat[i][j + 1] == 1)
        return 0;

    return 1;
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1 && is_isolated(i, j, mat))
                return 0;
        }
    }

    return 1;
}

int main() {
    int mat[8][8] = {{0}};
    generate_matrix(0, 0, mat);
    printf("Number of unholy 8x8 matrices: %d\n", count);

    return 0;
}
Please note that the above program may take a long time to run because it needs to check 2^64 (18,446,744,073,709,551,616) matrices. You can try running the program for smaller matrices (e.g., 4x4 or 5x5) to see if it works correctly and then decide whether you want to wait for the 8x8 result.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0;

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_isolated(int i, int j, int mat[8][8]) {
    if (i > 0 && mat[i - 1][j] == 1)
        return 0;
    if (i < 7 && mat[i + 1][j] == 1)
        return 0;
    if (j > 0 && mat[i][j - 1] == 1)
        return 0;
    if (j < 7 && mat[i][j + 1] == 1)
        return 0;

    return 1;
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1 && is_isolated(i, j, mat))
                return 0;
        }
    }

    return 1;
}

int main() {
    int mat[8][8] = {{0}};
    generate_matrix(0, 0, mat);
    printf("Number of unholy 8x8 matrices: %d\n", count);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0;

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_isolated(int i, int j, int mat[8][8]) {
    if (i > 0 && mat[i - 1][j] == 1)
        return 0;
    if (i < 7 && mat[i + 1][j] == 1)
        return 0;
    if (j > 0 && mat[i][j - 1] == 1)
        return 0;
    if (j < 7 && mat[i][j + 1] == 1)
        return 0;

    return 1;
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1 && is_isolated(i, j, mat))
                return 0;
        }
    }

    return 1;
}

int main() {
    int mat[8][8] = {{0}};
    generate_matrix(0, 0, mat);
    printf("Number of unholy 8x8 matrices: %d\n", count);

    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

Output

Here's a C program that counts the total number of unholy 8x8 binary matrices. The program uses a recursive function to generate and check all possible matrices. 

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#include <stdio.h>

#define SIZE 8

int count = 0;

void generate_matrix(int matrix[SIZE][SIZE], int row, int col) {
    if (row == SIZE) {
        count++;
        return;
    }

    if (col == SIZE) {
        generate_matrix(matrix, row + 1, 0);
        return;
    }

    matrix[row][col] = 0;
    generate_matrix(matrix, row, col + 1);

    matrix[row][col] = 1;
    if (row > 0 && matrix[row - 1][col] == 1) {
        generate_matrix(matrix, row, col + 1);
    } else if (col > 0 && matrix[row][col - 1] == 1) {
        generate_matrix(matrix, row, col + 1);
    }
}

int main() {
    int matrix[SIZE][SIZE] = {{0}};
    generate_matrix(matrix, 0, 0);
    printf("The total number of unholy 8x8 matrices is: %d\n", count);
    return 0;
}
The program defines an 8x8 matrix and initializes it with zeros. The `generate_matrix` function is called with the initial matrix and starting row and column indices (0, 0). The function generates all possible matrices by recursively setting the current cell to 0 or 1 and moving to the next cell. When a matrix is fully generated (i.e., all cells have been assigned a value), the function checks if it is unholy. If it is, the global `count` variable is incremented. The function uses the fact that a matrix is unholy if and only if there is no isolated 1, and a 1 is isolated if and only if there is no 1 in the cell above it or to its left. This allows the function to check for unholiness while generating the matrix, without the need for an additional checking function. Finally, the `main` function prints the total number of unholy matrices.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define SIZE 8

int count = 0;

void generate_matrix(int matrix[SIZE][SIZE], int row, int col) {
    if (row == SIZE) {
        count++;
        return;
    }

    if (col == SIZE) {
        generate_matrix(matrix, row + 1, 0);
        return;
    }

    matrix[row][col] = 0;
    generate_matrix(matrix, row, col + 1);

    matrix[row][col] = 1;
    if (row > 0 && matrix[row - 1][col] == 1) {
        generate_matrix(matrix, row, col + 1);
    } else if (col > 0 && matrix[row][col - 1] == 1) {
        generate_matrix(matrix, row, col + 1);
    }
}

int main() {
    int matrix[SIZE][SIZE] = {{0}};
    generate_matrix(matrix, 0, 0);
    printf("The total number of unholy 8x8 matrices is: %d\n", count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

#define SIZE 8

int count = 0;

void generate_matrix(int matrix[SIZE][SIZE], int row, int col) {
    if (row == SIZE) {
        count++;
        return;
    }

    if (col == SIZE) {
        generate_matrix(matrix, row + 1, 0);
        return;
    }

    matrix[row][col] = 0;
    generate_matrix(matrix, row, col + 1);

    matrix[row][col] = 1;
    if (row > 0 && matrix[row - 1][col] == 1) {
        generate_matrix(matrix, row, col + 1);
    } else if (col > 0 && matrix[row][col - 1] == 1) {
        generate_matrix(matrix, row, col + 1);
    }
}

int main() {
    int matrix[SIZE][SIZE] = {{0}};
    generate_matrix(matrix, 0, 0);
    printf("The total number of unholy 8x8 matrices is: %d\n", count);
    return 0;
}
And got the output: The total number of unholy 8x8 matrices is: 1

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.

Output

Here is a C program that counts the total number of unholy 8x8 matrices. This program uses recursion to generate all possible 8x8 matrices and then checks if they are unholy or not. 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0; // global variable to store the total count

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (i == 7 || mat[i + 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (j == 7 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }

    return 1;
}

int main() {
    int mat[8][8];
    generate_matrix(0, 0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}
This program may take a long time to run because there are 2^64 (approximately 1.8 x 10^19) possible 8x8 matrices.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0; // global variable to store the total count

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (i == 7 || mat[i + 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (j == 7 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }

    return 1;
}

int main() {
    int mat[8][8];
    generate_matrix(0, 0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(int mat[8][8]);

int count = 0; // global variable to store the total count

void generate_matrix(int i, int j, int mat[8][8]) {
    if (i == 8) {
        count += is_unholy(mat);
        return;
    }

    if (j == 8) {
        generate_matrix(i + 1, 0, mat);
        return;
    }

    mat[i][j] = 0;
    generate_matrix(i, j + 1, mat);

    mat[i][j] = 1;
    generate_matrix(i, j + 1, mat);
}

int is_unholy(int mat[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (mat[i][j] == 1) {
                if ((i == 0 || mat[i - 1][j] == 0) &&
                    (i == 7 || mat[i + 1][j] == 0) &&
                    (j == 0 || mat[i][j - 1] == 0) &&
                    (j == 7 || mat[i][j + 1] == 0)) {
                    return 0;
                }
            }
        }
    }

    return 1;
}

int main() {
    int mat[8][8];
    generate_matrix(0, 0, mat);
    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False