# Problem D: Power Strings

Problem D: Power Strings ## Problem D: Power Strings

Given two strings a and b we define a*b to be their concatenation. For example, if a = "abc" and b = "def" then a*b = "abcdef". If we think of concatenation as multiplication, exponentiation by a non-negative integer is defined in the normal way: a^0 = "" (the empty string) and a^(n+1) = a*(a^n).

Each test case is a line of input representing s, a string of printable characters. For each s you should print the largest n such that s = a^n for some string a. The length of s will be at least 1 and will not exceed 1 million characters. A line containing a period follows the last test case.

``````abcd
aaaa
ababab
.
``````

``````1
4
3
``````

``````#include <stdio.h>

main(){
int n,i,sum;
while (1 == scanf("%d",&n) && n) {
sum = n;
for (i=2;i*i <= n;i++) {
if (n%i == 0) {
sum -= sum/i;
}
while (n%i == 0) n /= i;
}
if (n > 1) sum -= sum/n;
printf("%d\n",sum);
}
}
``````

``````#include <stdio.h>

main(){
int n,i,sum;
while (1 == scanf("%d",&n) && n) {
sum = n;
for (i=2;i*i <= n;i++) {
if (n%i == 0) {
sum -= sum/i;
}
while (n%i == 0) n /= i;
}
if (n > 1) sum -= sum/n;
printf("%d\n",sum);
}
}
``````