/*
Reference:
競プロ初心者日記 #25「World Tour Finals2019 Eの解説を解説する」
https://www.nicovideo.jp/watch/sm35888883

ｺﾄﾉﾊｼﾏｲｶｼｺｲﾔｯﾀｰ
*/

//#define _GLIBCXX_DEBUG
#include "bits/stdc++.h"

using namespace std;

//------------------------------- Libraries --------------------------------//

template <int p>
struct Modint
{
    int value;

    Modint() : value(0) {}
    Modint(long x) : value(x >= 0 ? x % p : (p + x % p) % p) {}

    inline Modint &operator+=(const Modint &b)
    {
        if ((this->value += b.value) >= p)
            this->value -= p;
        return (*this);
    }
    inline Modint &operator-=(const Modint &b)
    {
        if ((this->value += p - b.value) >= p)
            this->value -= p;
        return (*this);
    }
    inline Modint &operator*=(const Modint &b)
    {
        this->value = (int)((1LL * this->value * b.value) % p);
        return (*this);
    }
    inline Modint &operator/=(const Modint &b)
    {
        (*this) *= b.inverse();
        return (*this);
    }

    Modint operator+(const Modint &b) const { return Modint(*this) += b; }
    Modint operator-(const Modint &b) const { return Modint(*this) -= b; }
    Modint operator*(const Modint &b) const { return Modint(*this) *= b; }
    Modint operator/(const Modint &b) const { return Modint(*this) /= b; }

    inline Modint &operator++(int) { return (*this) += 1; }
    inline Modint &operator--(int) { return (*this) -= 1; }

    inline bool operator==(const Modint &b) const
    {
        return this->value == b.value;
    }
    inline bool operator!=(const Modint &b) const
    {
        return this->value != b.value;
    }
    inline bool operator<(const Modint &b) const
    {
        return this->value < b.value;
    }
    inline bool operator<=(const Modint &b) const
    {
        return this->value <= b.value;
    }
    inline bool operator>(const Modint &b) const
    {
        return this->value > b.value;
    }
    inline bool operator>=(const Modint &b) const
    {
        return this->value >= b.value;
    }

    // requires that "this->value and p are co-prime"
    // a_i * v + a_(i+1) * p = r_i
    // r_i = r_(i+1) * q_(i+1) * r_(i+2)
    // q == 1 (i > 1)
    // reference: https://atcoder.jp/contests/agc026/submissions/2845729
    // (line:93)
    inline Modint inverse() const
    {
        assert(this->value != 0);
        int r0 = p, r1 = this->value, a0 = 0, a1 = 1;
        while (r1)
        {
            int q = r0 / r1;
            r0 -= q * r1;
            swap(r0, r1);
            a0 -= q * a1;
            swap(a0, a1);
        }
        return Modint(a0);
    }

    friend istream &operator>>(istream &is, Modint<p> &a)
    {
        long t;
        is >> t;
        a = Modint<p>(t);
        return is;
    }
    friend ostream &operator<<(ostream &os, const Modint<p> &a)
    {
        return os << a.value;
    }
};

/*
verified @ https://atcoder.jp/contests/abc034/submissions/4316971
*/

const int MOD = 1e9 + 7;

using Int = Modint<MOD>;

//------------------------------- Type Names -------------------------------//

using i64 = int_fast64_t;

using seika = string;
//akari : 1D, yukari : 2D, maki : 3D vector
template <class kizuna>
using akari = vector<kizuna>;
template <class yuzuki>
using yukari = akari<akari<yuzuki>>;
template <class tsurumaki>
using maki = akari<yukari<tsurumaki>>;
//akane : ascending order, aoi : decending order
template <class kotonoha>
using akane = priority_queue<kotonoha, akari<kotonoha>, greater<kotonoha>>;
template <class kotonoha>
using aoi = priority_queue<kotonoha>;

//------------------------------- Dubug Functions ---------------------------//
inline void print()
{
    cout << endl;
}
template <typename First, typename... Rest>
void print(const First &first, const Rest &... rest)
{
    cout << first << ' ';
    print(rest...);
}
//------------------------------- Solver ------------------------------------//

void integrate(akari<Int> &P, akari<Int> &Q, Int &C, const akari<Int> &P1, const akari<Int> &Q1, const Int &C1, int m, bool up)
{
    if (up)
    {
        for (int i = 0; i <= m; i++)
        {
            P[0] += P1[i] / Int(i + 1);
            P[i + 1] += P1[i] / Int(-(i + 1));
        }
        for (int i = 0; i <= m; i++)
        {
            Q[0] += Q1[i] / Int(i + 1);
            Q[i + 1] += Q1[i] / Int(-(i + 1));
        }
        Q[0] -= C1;
        C += C1;
    }
    else
    {
        for (int i = 0; i <= m; i++)
        {
            P[i + 1] += P1[i] / Int(i + 1);
        }
        for (int i = 0; i <= m; i++)
        {
            Q[i + 1] += Q1[i] / Int(i + 1);
        }
        P[0] += C1;
        C -= C1;
    }
}

void solve()
{
    int n;
    seika s;
    cin >> n >> s;

    maki<akari<Int>> Ps(2, yukari<akari<Int>>(2, akari<akari<Int>>(2, akari<Int>(1)))), Qs(Ps);
    maki<Int> C(2, yukari<Int>(2, akari<Int>(2)));

    Ps[1][1][1][0] = 1;
    C[0][1][1] = 1;
    C[1][1][1] = -1;
    for (int i = 0; i < n; i++)
    {
        maki<akari<Int>> nxPs(2, yukari<akari<Int>>(2, akari<akari<Int>>(2, akari<Int>(i + 2)))), nxQs(nxPs);
        maki<Int> nxC(2, yukari<Int>(2, akari<Int>(2)));
        if (s[i] == 'X')
        {
            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[0][0][1], Qs[0][0][1], C[0][0][1], i, true);
            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[0][1][1], Qs[0][1][1], C[0][1][1], i, true);
            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[1][0][1], Qs[1][0][1], C[1][0][1], i, true);
            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[1][1][1], Qs[1][1][1], C[1][1][1], i, true);

            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[1][1][0], Qs[1][1][0], C[1][1][0], i, false);
            integrate(nxPs[0][1][0], nxQs[0][1][0], nxC[0][1][0], Ps[1][1][1], Qs[1][1][1], C[1][1][1], i, false);
        }
        else
        {
            integrate(nxPs[1][1][1], nxQs[1][1][1], nxC[1][1][1], Ps[0][1][0], Qs[0][1][0], C[0][1][0], i, false);
            integrate(nxPs[1][1][1], nxQs[1][1][1], nxC[1][1][1], Ps[0][1][1], Qs[0][1][1], C[0][1][1], i, false);

            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[0][1][0], Qs[0][1][0], C[0][1][0], i, true);
            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[0][1][1], Qs[0][1][1], C[0][1][1], i, true);
            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[1][1][0], Qs[1][1][0], C[1][1][0], i, true);
            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[1][1][1], Qs[1][1][1], C[1][1][1], i, true);

            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[1][1][0], Qs[1][1][0], C[1][1][0], i, false);
            integrate(nxPs[0][0][1], nxQs[0][0][1], nxC[0][0][1], Ps[1][1][1], Qs[1][1][1], C[1][1][1], i, false);
        }
        swap(Ps, nxPs);
        swap(Qs, nxQs);
        swap(C, nxC);
    }

    akari<Int> ans(3);
    //I_k = a_k + b_k / e
    Int a = 1, b = Int(-1);
    for (int i = 0; i <= n; i++)
    {
        //[1][1]
        ans[0] += Ps[0][1][1][i] / Int(i + 1);
        ans[0] += Ps[1][1][1][i] / Int(i + 1);
        ans[1] += Qs[0][1][1][i] / Int(i + 1);
        ans[1] += Qs[1][1][1][i] / Int(i + 1);
        if (!i)
        {
            ans[0] += C[0][1][1] + C[1][1][1];
            ans[1] -= C[0][1][1] + C[1][1][1];
        }

        //[0][1]
        ans[0] += Ps[0][0][1][i] / Int(i + 1);
        ans[0] += Ps[1][0][1][i] / Int(i + 1);
        ans[1] += Qs[0][0][1][i] / Int(i + 1);
        ans[1] += Qs[1][0][1][i] / Int(i + 1);
        if (!i)
        {
            ans[0] += C[0][0][1] + C[1][0][1];
            ans[1] -= C[0][0][1] + C[1][0][1];
        }

        ans[0] -= Ps[0][0][1][i] * a;
        ans[0] -= Ps[1][0][1][i] * a;
        ans[1] -= Qs[0][0][1][i] * a;
        ans[1] -= Qs[1][0][1][i] * a;

        ans[1] -= Ps[0][0][1][i] * b;
        ans[1] -= Ps[1][0][1][i] * b;
        ans[2] -= Qs[0][0][1][i] * b;
        ans[2] -= Qs[1][0][1][i] * b;
        if (!i)
        {
            ans[0] -= (C[0][0][1] + C[1][0][1]) / 2;
            ans[2] += (C[0][0][1] + C[1][0][1]) / 2;
        }

        //[1][0]
        ans[0] += Ps[0][1][0][i] * a;
        ans[0] += Ps[1][1][0][i] * a;
        ans[1] += Qs[0][1][0][i] * a;
        ans[1] += Qs[1][1][0][i] * a;

        ans[1] += Ps[0][1][0][i] * b;
        ans[1] += Ps[1][1][0][i] * b;
        ans[2] += Qs[0][1][0][i] * b;
        ans[2] += Qs[1][1][0][i] * b;
        if (!i)
        {
            ans[0] += (C[0][1][0] + C[1][1][0]) / 2;
            ans[2] -= (C[0][1][0] + C[1][1][0]) / 2;
        }

        a *= i + 1;
        b = Int(i + 1) * b - 1;
    }
    print(ans[0], ans[1], ans[2]);
}

int main()
{
    solve();
    return 0;
}

Measured memory_bytes: 384