#include <bits/stdc++.h>

using namespace std;

char nl = '\n';
char sp = ' ';
using ll = long long;
using vb = vector<bool>;
using vi = vector<int>;
using vl = vector<ll>;
using vvb = vector<vb>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using si = unordered_set<int>;
using sl = unordered_set<ll>;
using tsi = set<int>;
using tsl = set<ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using tmii = map<int, int>;
using tmll = map<ll, ll>;
using mii = unordered_map<int, int>;
using mll = unordered_map<ll, ll>;
using pqi = priority_queue<int>;
using pqig = priority_queue<int, vi, greater<int>>;
using pql = priority_queue<ll>;
using pqlg = priority_queue<ll, vl, greater<ll>>;
using pqpii = priority_queue<pii>;
using pqpll = priority_queue<pll>;

#define tp3(T) tuple<T,T,T>
#define tp4(T) tuple<T,T,T,T>

#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define outrange(x,min,max) ((x)<(min) || (x)>(max))

ll _start_time;
#define nano (chrono::system_clock::now().time_since_epoch().count())
#define reset_timer _start_time=nano
#define chime cout<<((nano-_start_time)/1e9)<<endl
#define init_rng mt19937 rng(nano)
#define randint(a,b) ((a)+rng()%((b)-(a)+1))

#ifndef ONLINE_JUDGE
#define debug(x) (cout<<(#x)<<':'<<(x)<<'\n')
#else
#define debug(x)
#endif

void yesno(bool a) {
	cout << (a ? "Yes\n" : "No\n");
}

template<typename L, typename R>
ostream& operator<<(ostream& out, const pair<L, R>& p) {
	out << '(' << p.first << ',' << p.second << ')';
	return out;
}

template<typename T1, typename T2, typename T3>
ostream& operator<<(ostream& out, const tuple<T1, T2, T3>& tp) {
	auto [t1, t2, t3] = tp;
	out << '(' << t1 << ',' << t2 << ',' << t3 << ')';
	return out;
}

template<typename T>
ostream& operator<<(ostream& out, const vector<T>& v) {
	for (auto &i : v) out << i << ' ';
	out << nl;
	return out;
}

template<typename T>
ostream& operator<<(ostream& out, const set<T>& v) {
	for (auto &i : v) out << i << ' ';
	out << nl;
	return out;
}

template<typename T>
ostream& operator<<(ostream& out, const unordered_set<T>& v) {
	for (auto &i : v) out << i << ' ';
	out << nl;
	return out;
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const map<K, V>& m) {
	out << '[';
	for (auto &[k, v] : m) {
		out << k << ':' << v << sp;
	}
	out << "]\n";
	return out;
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const unordered_map<K, V>& m) {
	out << '[';
	for (auto &[k, v] : m) {
		out << k << ':' << v << sp;
	}
	out << "]\n";
	return out;
}

using u64 = unsigned long long;

u64 pow_10[]={1, 10, 100, 1000, 10000, 100'000, 1'000'000,
	10'000'000, 100'000'000, 1'000'000'000};

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	u64 A,B,N;
//	cin>>A>>B>>N;
	A=pow_10[5];
	B=pow_10[5];
	N=pow_10[9];
	vector<vector<u64>> b_factors(100001,vector<u64>());
	vector<vector<u64>> factors(10,vector<u64>());
	
	for(int i=1;i<=100000;i++){
		for(int j=i;j<=100000;j+=i){
			b_factors[j].push_back(i);
		}
	}
	
	for(int digit_n=1;digit_n<=9;digit_n++){
		int t=pow_10[digit_n]-1;
		for(int i=1;i*i<=t;i++){
			int j=t/i;
			if(i*j!=t) continue;
			factors[digit_n].push_back(i);
			if(i!=j) factors[digit_n].push_back(j);
		}
	}
	u64 ans=0;
	
	unordered_set<u64> checked;
	vector<tp3(int)> v;
	for(int digit_b=1;digit_b<=5;digit_b++){
		u64 pow10_b=pow_10[digit_b];
		for(u64 b=pow10_b/10;b<min(B,pow10_b);b++){

			//The whole process could cost over 30 seconds, so we need to 
			//know how many values of b we've processed.
			if(b%100==0) cout<<b<<endl;
			
			for(int digit_n=1;digit_n<=9;digit_n++){
				checked.clear();
				for(u64 d1:b_factors[b]){
					for(u64 d2:factors[digit_n]){
						u64 d=d1*d2;
						if(d<pow10_b-b) continue;
						if(checked.count(d)) {
							continue;
						}
						
						checked.insert(d);
						
						u64 r=pow10_b-d%pow10_b;
						if(b%r!=0) continue;
						u64 c=b/r;
						u64 k=(d+r)/pow10_b;
						u64 a=k*c;
						if(a>=A || c!=gcd(a,b)) continue;
						u64 n=k*b*(pow_10[digit_n]-1)/(pow10_b*k-r);
						if(pow_10[digit_n-1]<=n && n<N && n<pow_10[digit_n]) {
							ans++;
							v.emplace_back(a,b,n);
						}
					}
				}
			}
		}
	}
	cout<<ans<<nl;
	
	// Output special values of b.
	ofstream ofs;
	ofs.open("D:\\PandaCpp\\Codeforces\\my_out.txt");
	sort(all(v));
	set<u64> s;
	int t=0;
	for(auto [a,b,n]:v){
		if(b==a || b==10*a || b==100*a || b==1000*a || b==10000*a) continue;
		if(a==b || a==10*b || a==100*b || a==1000*b || a==10000*b) continue;
		if(s.count(b)) continue;
		ofs<<b<<',';
		t++;
		if(t%20==0) ofs<<nl;
		s.insert(b);
	}
}