11687 - Digits

Problem D: Digits

A googol written out in decimal has 101 digits. A googolplex hasone plus a googol digits. That's a lot of digits!

Given any number x₀, define a sequenceusing the following recurrence:

x_i+1 = the number of digits in the decimal representation of x_i

Your task is to determine the smallest positive i such thatx_i = x_i-1.

Input Specification

Input consists of several lines. Each line contains avalue of x₀. Every value of x₀is non-negative and has no more than one million digits.The last line of input containsthe word END.

Sample Input

42
END

Output Specification

For each value of x₀ given in the input, outputone line containing the smallest positive i such that x_i = x_i-1.

Output for Sample Input

3

#include
#include
char a[10000010];
int p;
int solve(int x)
{ 
	int y;
	sprintf(a,"%d",x);
	y=strlen(a);
	p++;
	if(x==y) return p;
	solve(y);
}
int main()
{
	while(gets(a)){
		p=1;
		if(strcmp(a,"END")==0) break;
		else if(strcmp(a,"1")==0) puts("1");
		else printf("%d\n",solve(strlen(a)));
	}
	return 0;
}