Coconuts 1
Difficulty: Hard

The short story titled Coconuts, by Ben Ames Williams, tells about five men and a monkey who were shipwrecked on an island. They spent the first night gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share and went back to sheep.  

Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. This time no coconuts were left over.

An obvious question is "how many coconuts did they originally gather?" There are an infinite number of answers, but the lowest of these is 3,121. But that's not our problem here.
Suppose we turn the problem around. If we know the number of coconuts that were gathered, what is the maximum number of persons (and one monkey) that could have been shipwrecked if the same procedure could occur?

**Input Format:**
The input will consist of a sequence of integers, each representing the number of coconuts gathered by a group of persons (and a monkey) that were shipwrecked. The sequence will be followed by a negative number.

**Output Format:**
For each number of coconuts, determine the largest number of persons who could have participated in the procedure described above. Display the results similar to the manner shown below, in the Expected Output. There may be no solution for some of the input cases; if so, state that observation.

**Sample Input:**  
25  
30  
3121  
-1		  

**Expected Input:**  
25 coconuts, 3 persons and 1 monkey  
30 coconuts, no solution  
3121 coconuts, 5 persons and 1 monkey  






Input Format:

Output Format:

Sample Input:

Sample Output:

Python 3 starter code:


Reference solution (C++):
    #include <stdio.h>

    /* return 1 if this number of coconuts can be divided up
       properly between this number of people */
    int SplitCoco(long n_coco, long n_people) {
    long i;

    for (i=0; i<n_people; i++) {
            /* check that the coconuts divide by the number of people
               plus one remainder */
        if (n_coco % n_people != 1) return 0;
            /* remove 1 for the monkey, and one person's share */
        n_coco = n_coco - 1 - (n_coco / n_people);
    }
        /* check that the remaining coconuts divide evenly among
           the people */
    return (n_coco % n_people) == 0;    
    }

    int main() {
    long n_coco;
    long n_people;
    long i, j, k;

    /* FILE *inf = fopen("prob_3.in", "r"); */
    FILE *inf = stdin;

    while (fscanf(inf, "%ld", &n_coco), n_coco!=-1) {
            /* starting at the # of coconuts-1, count down until
               a number of people is found that works */
        for (n_people=n_coco-1; n_people > 1; n_people--) {
            if (SplitCoco(n_coco, n_people)) {
                printf("%ld coconuts, %ld people and 1 monkey\n",
                    n_coco, n_people);
                goto found;

                /* OK, so yea, I put a 'goto' in my code :-)
                   it was quick and it works.  I don't do
                   it often, I swear. */

            }
        }
            /* if no number of people greater than 1 works, there is
               no solution */
        printf("%ld coconuts, no solution\n", n_coco);
        found:
    }
    return 0;
    }