#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) { 
	bool fst = 1; str res = "{";
	F0R(i,sz(v)) {
		if (!fst) res += ", ";
		fst = 0; res += ts(v[i]);
	}
	res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
	str res = ""; F0R(i,SZ) res += char('0'+b[i]);
	return res; }
template<class T> str ts(T v) {
	bool fst = 1; str res = "{";
	for (const auto& x: v) {
		if (!fst) res += ", ";
		fst = 0; res += ts(x);
	}
	res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
	return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
	pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
	pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
	cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
	DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
	unsyncIO();
	// cin.exceptions(cin.failbit); 
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

/**
 * Description: modular arithmetic operations 
 * Source: 
	* KACTL
	* https://codeforces.com/blog/entry/63903
	* https://codeforces.com/contest/1261/submission/65632855 (tourist)
	* https://codeforces.com/contest/1264/submission/66344993 (ksun)
 * Verification: 
	* https://open.kattis.com/problems/modulararithmetic
 */

struct mi {
	typedef decay<decltype(MOD)>::type T; 
 	/// don't silently convert to T
	T v; explicit operator T() const { return v; }
	mi() { v = 0; }
	mi(ll _v) { 
		v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
		if (v < 0) v += MOD;
	}
	friend bool operator==(const mi& a, const mi& b) { 
		return a.v == b.v; }
	friend bool operator!=(const mi& a, const mi& b) { 
		return !(a == b); }
	friend bool operator<(const mi& a, const mi& b) { 
		return a.v < b.v; }
	friend void re(mi& a) { ll x; re(x); a = mi(x); }
	friend str ts(mi a) { return ts(a.v); }
   
	mi& operator+=(const mi& m) { 
		if ((v += m.v) >= MOD) v -= MOD; 
		return *this; }
	mi& operator-=(const mi& m) { 
		if ((v -= m.v) < 0) v += MOD; 
		return *this; }
	mi& operator*=(const mi& m) { 
		v = (ll)v*m.v%MOD; return *this; }
	mi& operator/=(const mi& m) { return (*this) *= inv(m); }
	friend mi pow(mi a, ll p) {
		mi ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans;
	}
	friend mi inv(const mi& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mi operator-() const { return mi(-v); }
	mi& operator++() { return *this += 1; }
	mi& operator--() { return *this -= 1; }
	friend mi operator+(mi a, const mi& b) { return a += b; }
	friend mi operator-(mi a, const mi& b) { return a -= b; }
	friend mi operator*(mi a, const mi& b) { return a *= b; }
	friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;

vector<vmi> comb;
void genComb(int SZ) {
	comb.assign(SZ,vmi(SZ)); comb[0][0] = 1;
	FOR(i,1,SZ) F0R(j,i+1) 
		comb[i][j] = comb[i-1][j]+(j?comb[i-1][j-1]:0);
}

/**
 * Description: Basic poly ops including division and interpolation.
 * Source: Own. Also see
 	* https://github.com/kth-competitive-programming/kactl/blob/master/content/numerical/PolyInterpolate.h
 	* https://github.com/ecnerwala/icpc-book/blob/master/content/numerical/fft.cpp
 * Verification: see FFT
 */

typedef mi T; using poly = vector<T>;
void remz(poly& p) { while (sz(p) && p.bk==0) p.pop_back(); }
poly rev(poly p) { reverse(all(p)); return p; }
poly shift(poly p, int x) { p.insert(begin(p),x,0); return p; }
poly RSZ(poly p, int x) { p.rsz(x); return p; }
T eval(const poly& p, T x) {
	T res = 0; R0F(i,sz(p)) res = x*res+p[i]; 
	return res; }
poly dif(const poly& p) { // differentiate
	poly res; FOR(i,1,sz(p)) res.pb(i*p[i]); 
	return res; }
poly integ(const poly& p) { // integrate
	poly res(sz(p)+1); F0R(i,sz(p)) res[i+1] = p[i]/(i+1);
	return res; }

poly& operator+=(poly& l, const poly& r) {
	l.rsz(max(sz(l),sz(r))); F0R(i,sz(r)) l[i] += r[i]; 
	return l; }
poly& operator-=(poly& l, const poly& r) {
	l.rsz(max(sz(l),sz(r))); F0R(i,sz(r)) l[i] -= r[i]; 
	return l; }
poly& operator*=(poly& l, const T& r) { trav(t,l) t *= r; 
	return l;	 }
poly& operator/=(poly& l, const T& r) { trav(t,l) t /= r; 
	return l; }
poly operator+(poly l, const poly& r) { return l += r; }
poly operator-(poly l, const poly& r) { return l -= r; }
poly operator-(poly l) { trav(t,l) t *= -1; return l; }
poly operator*(poly l, const T& r) { return l *= r; }
poly operator*(const T& r, const poly& l) { return l*r; }
poly operator/(poly l, const T& r) { return l /= r;	 }
poly operator*(const poly& l, const poly& r) {
	if (!min(sz(l),sz(r))) return {};
	poly x(sz(l)+sz(r)-1); 
	F0R(i,sz(l)) F0R(j,sz(r)) x[i+j] += l[i]*r[j];
	return x;
}
poly& operator*=(poly& l, const poly& r) { return l = l*r; }

pair<poly,poly> quoRem(poly a, poly b) { 
	assert(sz(b)); auto B = b.bk; assert(B != 0);
	B = 1/B; trav(t,b) t *= B;
	remz(a); poly q(max(sz(a)-sz(b)+1,0));
	while (sz(a) >= sz(b)) {
		q[sz(a)-sz(b)] = a.bk;
		F0R(i,sz(b)) a[i+sz(a)-sz(b)] -= a.bk*b[i];
		remz(a);
	}
	trav(t,q) t *= B; 
	return {q,a};
}
poly interpolate(vector<pair<T,T>> v) {
	poly ret, prod = {1}; trav(t,v) prod *= poly({-t.f,1});
	F0R(i,sz(v)) {
		T fac = 1; F0R(j,sz(v)) if (i != j) fac *= v[i].f-v[j].f;
		ret += v[i].s/fac*quoRem(prod,{-v[i].f,1}).f;
	}
	return ret;
}

int N;
str s;

array<mi,3>& operator+=(array<mi,3>& a, array<mi,3> b) {
	F0R(i,3) a[i] += b[i];
	return a;
}
array<mi,3> operator-(array<mi,3> a, array<mi,3> b) {
	F0R(i,3) a[i] -= b[i];
	return a;
}

pmi int1(poly p) {
	pmi res = {0,0};
	if (!sz(p)) return res;
	vpmi mem(sz(p)); mem[0] = {1,-1};
	FOR(i,1,sz(p)) {
		mem[i] = {i*mem[i-1].f,i*mem[i-1].s};
		mem[i].s -= 1;
	}
	F0R(i,sz(p)) {
		pmi z = mem[i];
		res.f += p[i]*z.f;
		res.s += p[i]*z.s;
	}
	return res;
}

struct stor {
	poly p,q; mi c;
	stor operator-(const stor& b) { return {p-b.p,q-b.q,c-b.c}; }
	stor operator+(const stor& b) { return {p+b.p,q+b.q,c+b.c}; }
	stor& operator+=(const stor& b) { return (*this) = (*this)+b; }
	stor int0x() {
		stor res;
		res.p = integ(p); res.q = integ(q);
		res.p += poly{c}; res.c = -c;
		return res;
	}
	stor intx1() {
		stor res;
		res.p = poly{eval(integ(p),1)}-integ(p);
		res.q = poly{eval(integ(q),1)}-integ(q);
		res.q -= poly{c}; res.c = c;
		return res;
	}
	array<mi,3> INT0() {
		return {eval(integ(p),1)+c,eval(integ(q),1)-c,0};
	}
	array<mi,3> INT1() {
		pmi a = int1(p), b = int1(q);
		return {a.f+c/2,a.s+b.f,b.s-c/2};
	}
	array<mi,3> INT2() {
		return INT0()-INT1();
	}
};

stor dp[1000][2][2][2]; // length to left, can be even, can be odd

stor one{{1},{},0}, enx{{},{},1};

int main() {
	setIO(); re(N,s);
	if (s[0] == 'X') {
		dp[0][0][1][0] = enx;
	} else {
		dp[0][0][0][1] = enx;
		dp[0][1][1][1] = one-enx;
	}
	FOR(i,1,N) {
		if (s[i] == 'X') { // run to left is even, run to right must be even
			// X[i-1] < X[i]
			F0R(a,2) dp[i][0][1][0] += dp[i-1][1][1][a].int0x();
			// X[i-1] > X[i]
			F0R(a,2) F0R(b,2) dp[i][0][1][0] += dp[i-1][a][b][1].intx1();
		} else {
			// decreasing run to left is odd or decreasing run to right is odd
			// X[i-1] < X[i]
			F0R(a,2) {
				// even run
				dp[i][0][0][1] += dp[i-1][1][1][a].int0x();
				// odd run
				dp[i][1][1][1] += dp[i-1][0][1][a].int0x();
			}
			// X[i-1] > X[i]
			F0R(a,2) F0R(b,2) dp[i][0][0][1] += dp[i-1][a][1][b].intx1();
		}
	}
	array<mi,3> res;
	F0R(a,2) {
		res += dp[N-1][a][1][1].INT0(); // integ from 0 to 1
		res += dp[N-1][a][1][0].INT1(); // times e^{-x}
		res += dp[N-1][a][0][1].INT2();
	}
	ps(res[0],res[1],res[2]);
	// you should actually read the stuff at the bottom
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
	* do smth instead of nothing and stay organized
	* WRITE STUFF DOWN
*/



Measured memory_bytes: 8064