#include <bits/stdc++.h> 

using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); i--)
#define SZ(a) int(a.size())
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first
#define S second

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

int a[3];

string s;
bool read()
{
	if(!(cin >> s))
		return false;
	
	s += "^";
	int prev = 0;
	int pos = 0;
	FOR(i, 0, SZ(s))
	{
		if(s[i] == '^')
		{
			//cerr << s << " " << pos << " " << prev << " " << i << "\n";
			a[pos] = stoi(s.substr(prev, i - prev));
			pos++;
			prev = i + 1;
			continue;
		}
	}
	return true;
}

vector<PII> factor(int x)
{
	vector<PII> res;
	for(int p = 2; p * p <= x; p++)
	{
		if(x % p)
			continue;
		int cnt = 0;
		while(x % p == 0)
		{
			x /= p;
			cnt++;
		}
		res.PB({p, cnt});
	}
	if(x != 1)
		res.PB({x, 1});
	return res;
}
const int N = 2e5;
int f[N];


void init()
{
	FOR(b, 2, N)
	{
		FOR(x, 2, N)
		{
			LL pw = 1;
			FOR(i, 0, b)
			{
				pw *= x;
				if(pw >= N)
					break;
			}
			if(pw >= N)
			{
				break;
			}
			f[pw] += f[b] + 1;
		}
	}
}

void solve()
{
	auto A = factor(a[0]);
	int k = 0;
	for(auto [p, c] : A) 
		k = gcd(k, c);
	
	map<int, int> cnt;	
	auto B = factor(a[1]);
	auto K = factor(k);
	for(auto [p, c] : B)
		cnt[p] += a[2] * c;
	for(auto [p, c] : K)
		cnt[p] += c;
	
	int mx = 0;
	for(auto [p, c] : cnt)
		mx = max(mx, c);
	
	
	LL ans = 0;
	FOR(c1, 2, mx + 1)
	{
		LL num = 1;
		for(auto [p, c] : cnt)
			num *= (c / c1 + 1);
		num -= 1;
		ans += num * (f[c1] + 1);
	}
	cout << ans << "\n";
}


int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	init();
	
	while(read())
		solve();
	
	
	
	
	return 0;
}