#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
using namespace std;
typedef long long LL;
static const LL MODVAL = 1234567891;
LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
LL FACT(LL x) { return x<=1 ? 1 : MUL(x, FACT(x-1)); }
class PSequence
{
public:
map<pair<vector<LL>,int>, LL> memo;
int count(vector <int> S, int p)
{
memo.clear();
vector<LL> cs; // congruences mod p
bool used[30] = {};
for(int i=0; i<S.size(); ++i)
if( !used[i] )
{
int cnt = 0;
for(int j=i; j<S.size(); ++j)
if( abs(S[i]-S[j]) % p == 0 )
{used[j]=true; ++cnt;}
cs.push_back(cnt);
}
LL f = num_perm( cs, -1, S.size() );
for(int i=0; i<cs.size(); ++i)
f = MUL(f, FACT(cs[i]));
return f;
}
LL num_perm( vector<LL>& cs, int forbidden, int n )
{
if( n == 0 )
return 1;
int v = (forbidden >= 0 ? cs[forbidden] : -1);
pair<vector<LL>,int> key(cs, forbidden);
sort(key.first.begin(), key.first.end());
key.second = find(key.first.begin(), key.first.end(), v) - key.first.begin();
if( memo.count(key) )
return memo[key];
LL np = 0;
for(int i=0; i<cs.size(); ++i)
if( cs[i] && i!=forbidden ) {
cs[i]--;
np = ADD(np, num_perm( cs, i, n-1 ));
cs[i]++;
}
return memo[key] = np;
}
// BEGIN CUT HERE
public:
void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
private:
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
void test_case_0() { int Arr0[] = {-1,0,1,2,3}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 10; int Arg2 = 120; verify_case(0, Arg2, count(Arg0, Arg1)); }
void test_case_1() { int Arr0[] = {6,2}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 4; int Arg2 = 0; verify_case(1, Arg2, count(Arg0, Arg1)); }
void test_case_2() { int Arr0[] = {1,2,3,4}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 3; int Arg2 = 12; verify_case(2, Arg2, count(Arg0, Arg1)); }
void test_case_3() { int Arr0[] = {4,6,8,-3,7}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 2; int Arg2 = 12; verify_case(3, Arg2, count(Arg0, Arg1)); }
void test_case_4() {
int Arr0[] = {0,1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29};
vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
int Arg1 = 15; int Arg2 = 12; verify_case(4, Arg2, count(Arg0, Arg1)); }
// END CUT HERE
};
// BEGIN CUT HERE
int main() { PSequence().run_test(-1); }
// END CUT HERE