#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
struct UnionFind
{
vector<int> uf, sz;
int nc;
UnionFind(int N) : uf(N), sz(N, 1), nc(N)
{
for (int i = 0; i<N; ++i) uf[i] = i;
}
int size()
{
return nc;
}
int size(int a)
{
return sz[Find(a)];
}
int Find(int a)
{
return uf[a] == a ? a : uf[a] = Find(uf[a]);
}
// Semi-compression w.o. recursion.
//{ while(uf[a] != a) a=uf[a]=uf[uf[a]]; return a; }
bool Union(int a, int b)
{
a = Find(a);
b = Find(b);
if (a != b)
{
if (sz[a] >= sz[b]) swap(a, b);
uf[a] = b;
sz[b] += sz[a];
--nc;
}
return (a != b);
}
};
static const unsigned MODVAL = 1000000007;
class DengklekGaneshAndTree { public:
int getCount(string labels, vector <int> parents)
{
const int N = labels.size();
vector<vector<int>> children(N);
UnionFind uf(N);
for (int i = 1; i < N; ++i) {
int u = parents[i-1], v = i;
children[u].push_back(v);
if (labels[u] == labels[v])
uf.Union(u, v);
}
vector<int> level(N);
{
function<void(int, int)> rec; rec = [&](int v, int lv) {
level[v] = lv;
for (int u : children[v])
rec(u, lv + 1);
};
rec(0, 0);
}
map<int, int> lb, ub;
for (int v = 0; v < N; ++v) {
int r = uf.Find(v), lv = level[v];
if (lb.count(r) == 0) {
lb[r] = lv;
ub[r] = lv;
}
else {
lb[r] = min(lb[r], lv);
ub[r] = max(ub[r], lv);
}
}
vector<pair<int, int>> rng;
for(auto kv : lb)
rng.emplace_back(kv.second, ub[kv.first]);
int L = *max_element(level.begin(), level.end());
return solve(rng, L);
}
// Number of ways to cover [0,L] by choosing subset of |rng|s.
int solve(vector<pair<int, int>> rng, int L) {
sort(rng.begin(), rng.end());
function<int(int, int)> rec;
vector<int> memo(rng.size() * (L+2), -1);
rec = [&](int i, int coveredUpto) {
if (i == rng.size())
return coveredUpto == L ? 1 : 0;
const int key = i*(L + 1) + (coveredUpto+1);
if (memo[key] != -1)
return memo[key];
if (coveredUpto + 2 <= rng[i].first)
return memo[key] = 0;
return memo[key] = (rec(i + 1, coveredUpto) + rec(i + 1, max(coveredUpto, rng[i].second))) % MODVAL;
};
return rec(0, -1);
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, DengklekGaneshAndTree().getCount(labels, parents));}
int main(){
CASE(0)
string labels = "seems";
int parents_[] = {0, 1, 0, 3};
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = 5;
END
CASE(1)
string labels = "like";
int parents_[] = {0, 0, 0};
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = 7;
END
CASE(2)
string labels = "a";
vector <int> parents;
int _ = 1;
END
CASE(3)
string labels = "coincidence";
int parents_[] = {0, 1, 2, 0, 2, 1, 4, 7, 7, 6};
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = 218;
END
CASE(4)
string labels = "topcoderopenroundtwobgoodluckhavefun";
int parents_[] = {0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0};
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = 147418098;
END
/*
CASE(5)
string labels = ;
int parents_[] = ;
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = ;
END
CASE(6)
string labels = ;
int parents_[] = ;
vector <int> parents(parents_, parents_+sizeof(parents_)/sizeof(*parents_));
int _ = ;
END
*/
}
// END CUT HERE