Nested Loops

We've seen for loops. Now let's put a loop inside another loop: a nested loop

#include <stdio.h>

int main(void) {
    for (int i = 1; i <= 3; i++) {
        for (int j = 1; j <= 3; j++) {
            printf("(%d, %d) ", i, j);
        }
        printf("\n");
    }
    return 0;
}

Output

(1, 1) (1, 2) (1, 3)
(2, 1) (2, 2) (2, 3)
(3, 1) (3, 2) (3, 3)

The outer loop controls the rows, the inner loop controls the columns. For every single value of i, the inner loop runs completely from start to finish. Read the output carefully and trace through the code in your head

A classic use of nested loops: printing a pattern

#include <stdio.h>

int main(void) {
    for (int i = 1; i <= 5; i++) {
        for (int j = 1; j <= i; j++) {
            printf("* ");
        }
        printf("\n");
    }
    return 0;
}

Output

*
* *
* * *
* * * *
* * * * *

Notice that the inner loop goes up to i, not up to 5. When i = 1, we print 1 star. When i = 3, we print 3 stars. This is how we build a triangle

Nested loops with arrays: imagine a multiplication table

#include <stdio.h>

int main(void) {
    int nums[] = {2, 3, 4};
    int n = 3;

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            printf("%d * %d = %d\n", nums[i], nums[j], nums[i] * nums[j]);
        }
    }
    return 0;
}

This prints every combination of two elements from the array. If the array has n elements, nested loops give us n * n combinations. When you hear "all pairs", think nested loops

Mission: The Line Printer Log

The computing center's line printer receives a job: the number of lines to print. Each line i must contain the numbers from 1 to i, as a print-head calibration test.

1. Read an integer n from input: the number of lines
2. Write nested for loops: the outer loop goes from 1 to n, the inner loop prints the numbers from 1 to i, separated by a space
3. Print printf("\n") at the end of each line

Example

Input

5

Output

1
1 2
1 2 3
1 2 3 4
1 2 3 4 5

Example

Input

3

Output

1
1 2
1 2 3