Hakone Ekiden is one of the Japanese New Year's traditions. In Hakone Ekiden, 10 runners from each team aim for the goal while connecting the sashes at each relay station. In the TV broadcast, the ranking change from the previous relay station is displayed along with the passing order of each team at the relay station. So, look at it and tell us how many possible passage orders for each team at the previous relay station. The number of possible transit orders can be very large, so answer by the remainder divided by 1,000,000,007.



Input

The input is given in the form:

> n
> c1
> c2
> ...
> cn
>

The number n (1 ≤ n ≤ 200) representing the number of teams is on the first line, and the ranking changes from the previous relay station in order from the first place on the following n lines. If it is'`U`', the ranking is up, if it is'`-`', the ranking is not changed) is written.

Output

Please output in one line by dividing the number of passages that could have been the previous relay station by 1,000,000,007.

Examples

Input

3
-
U
D


Output

1


Input

5
U
U
-
D
D


Output

5


Input

8
U
D
D
D
D
D
D
D


Output

1


Input

10
U
D
U
D
U
D
U
D
U
D


Output

608


Input

2
D
U


Output

0
#define  _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment (linker, "/STACK:526000000")

#include "bits/stdc++.h"

using namespace std;
typedef string::const_iterator State;
#define eps 1e-5L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()

// geometry library

typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;

typedef struct Circle {
    complex<long double> center;
    long double r;
}Circle;

long double dot(Point a, Point b) {
    return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
    return (a.real() * b.imag() - a.imag() * b.real());
}

long double Dist_Line_Point(Line a, Point b) {
    if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
    if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
    return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}

int is_intersected_ls(Line a, Line b) {
    return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < eps) &&
        (cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < eps);
}

Point intersection_l(Line a, Line b) {
    Point da = a.second - a.first;
    Point db = b.second - b.first;
    return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}

long double Dist_Line_Line(Line a, Line b) {
    if (is_intersected_ls(a, b) == 1) {
        return 0;
    }
    return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}

pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
    long double dist = abs(a.center - b.center);
    assert(dist <= eps + a.r + b.r);
    assert(dist + eps >= abs(a.r - b.r));
    Point target = b.center - a.center;
    long double pointer = target.real() * target.real() + target.imag() * target.imag();
    long double aa = pointer + a.r * a.r - b.r * b.r;
    aa /= 2.0L;
    Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
            (aa * target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
        (aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    r = r + a.center;
    l = l + a.center;
    return mp(l, r);
}

//end of geometry

template<typename A>
A pows(A val, ll b) {
    assert(b >= 1);
    A ans = val;
    b--;
    while (b) {
        if (b % 2) {
            ans *= val;
        }
        val *= val;
        b /= 2LL;
    }
    return ans;
}

template<typename A>
class Compressor {
public:
    bool is_zipped = false;
    map<A, ll> zipper;
    map<ll, A> unzipper;
    queue<A> fetcher;
    Compressor() {
        is_zipped = false;
        zipper.clear();
        unzipper.clear();
    }
    void add(A now) {
        assert(is_zipped == false);
        zipper[now] = 1;
        fetcher.push(now);
    }
    void exec() {
        assert(is_zipped == false);
        int cnt = 0;
        for (auto i = zipper.begin(); i != zipper.end(); ++i) {
            i->second = cnt;
            unzipper[cnt] = i->first;
            cnt++;
        }
        is_zipped = true;
    }
    ll fetch() {
        assert(is_zipped == true);
        A hoge = fetcher.front();
        fetcher.pop();
        return zipper[hoge];
    }
    ll zip(A now) {
        assert(is_zipped == true);
        assert(zipper.find(now) != zipper.end());
        return zipper[now];
    }
    A unzip(ll a) {
        assert(is_zipped == true);
        assert(a < unzipper.size());
        return unzipper[a];
    }
    ll next(A now) {
        auto x = zipper.upper_bound(now);
        if (x == zipper.end()) return zipper.size();
        return (ll)((*x).second);
    }
    ll back(A now) {
        auto x = zipper.lower_bound(now);
        if (x == zipper.begin()) return -1;
        x--;
        return (ll)((*x).second);
    }
};

template<typename A>
class Matrix {
public:
    vector<vector<A>> data;
    Matrix(vector<vector<A>> a) :data(a) {

    }
    Matrix operator + (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = obj.data[i][q] + (this->data[i][q]);
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator - (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = this->data[i][q] - obj.data[i][q];
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator * (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data[0].size());
        REP(i, this -> data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[0].size()) {
                A hoge = (this->data[i][0]) * (obj.data[0][q]);
                for (int t = 1; t < obj.data[i].size(); ++t) {
                    hoge += this->data[i][t] * obj.data[t][q];
                }
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix& operator *= (const Matrix obj) {
        *this = (*this * obj);
        return *this;
    }
    Matrix& operator += (const Matrix obj) {
        *this = (*this + obj);
        return *this;
    }
    Matrix& operator -= (const Matrix obj) {
        *this = (*this - obj);
        return *this;
    }
};

class modint {
public:
    using u64 = std::uint_fast64_t;
    u64 value = 0;
    u64 mod;
    modint(ll a, ll b) : value(((a% b) + 2 * b) % b), mod(b) {

    }
    modint operator+(const modint rhs) const {
        return modint(*this) += rhs;
    }
    modint operator-(const modint rhs) const {
        return modint(*this) -= rhs;
    }
    modint operator*(const modint rhs) const {
        return modint(*this) *= rhs;
    }
    modint operator/(const modint rhs) const {
        return modint(*this) /= rhs;
    }
    modint& operator+=(const modint rhs) {
        assert(rhs.mod == mod);
        value += rhs.value;
        if (value >= mod) {
            value -= mod;
        }
        return *this;
    }
    modint& operator-=(const modint rhs) {
        assert(rhs.mod == mod);
        if (value < rhs.value) {
            value += mod;
        }
        value -= rhs.value;
        return *this;
    }
    modint& operator*=(const modint rhs) {
        assert(rhs.mod == mod);
        value = (value * rhs.value) % mod;
        return *this;
    }
    modint& operator/=(modint rhs) {
        assert(rhs.mod == mod);
        ll rem = mod - 2;
        while (rem) {
            if (rem % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            rem /= 2LL;
        }
        return *this;
    }
    bool operator <(modint rhs) const {
        return value < rhs.value;
    }
    friend ostream& operator<<(ostream& os, modint& p) {
        os << p.value;
        return (os);
    }
};

class Dice {
public:
    vector<ll> vertexs;
    //Up: 0,Left: 1,Center: 2,Right: 3,Adj: 4, Down: 5
    Dice(vector<ll> init) :vertexs(init) {

    }
    //Look from Center
    void RtoL() {
        for (int q = 1; q < 4; ++q) {
            swap(vertexs[q], vertexs[q + 1]);
        }
    }
    void LtoR() {
        for (int q = 3; q >= 1; --q) {
            swap(vertexs[q], vertexs[q + 1]);
        }
    }
    void UtoD() {
        swap(vertexs[5], vertexs[4]);
        swap(vertexs[2], vertexs[5]);
        swap(vertexs[0], vertexs[2]);
    }
    void DtoU() {
        swap(vertexs[0], vertexs[2]);
        swap(vertexs[2], vertexs[5]);
        swap(vertexs[5], vertexs[4]);
    }
    bool ReachAble(Dice now) {
        set<Dice> hoge;
        queue<Dice> next;
        next.push(now);
        hoge.insert(now);
        while (next.empty() == false) {
            Dice seeing = next.front();
            next.pop();
            if (seeing == *this) return true;
            seeing.RtoL();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.LtoR();
            seeing.LtoR();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.RtoL();
            seeing.UtoD();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.DtoU();
            seeing.DtoU();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
        }
        return false;
    }
    bool operator ==(const Dice& a) {
        for (int q = 0; q < 6; ++q) {
            if (a.vertexs[q] != (*this).vertexs[q]) {
                return false;
            }
        }
        return true;
    }
    bool operator <(const Dice& a) const {
        return (*this).vertexs < a.vertexs;
    }
};

pair<Dice, Dice> TwoDimDice(int center, int up) {
    int target = 1;
    while (true) {
        if (center != target && 7 - center != target && up != target && 7 - up != target) {
            break;
        }
        target++;
    }
    return mp(Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}), Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}

tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
    int bo = min(center, 7 - center);
    pair<int, int> goa;
    if (bo == 1) {
        goa = mp(2, 3);
    }
    else if (bo == 2) {
        goa = mp(1, 3);
    }
    else if (bo == 3) {
        goa = mp(1, 2);
    }
    tuple<Dice, Dice, Dice, Dice> now = make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second, 7 - center, 7 - goa.first}),
        Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second, 7 - center, 7 - goa.first}),
        Dice(vector<ll>{7 - goa.first, goa.second, center, 7 - goa.second, 7 - center, goa.first}),
        Dice(vector<ll>{7 - goa.first, 7 - goa.second, center, goa.second, 7 - center, goa.first}));
    return now;
}

template<typename A, typename B>
class Dijkstra {
public:
    vector<vector<pair<int, A>>> vertexs;
    B Cost_Function;
    Dijkstra(int n, B cost) : Cost_Function(cost) {
        vertexs = vector<vector<pair<int, A>>>(n, vector<pair<int, A>>{});
    }
    ~Dijkstra() {
        vertexs.clear();
    }
    void add_edge(int a, int b, A c) {
        vertexs[a].push_back(mp(b, c));
    }
    vector<ll> build_result(int StartPoint) {
        vector<ll> dist(vertexs.size(), 2e18);
        dist[StartPoint] = 0;
        priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> next;
        next.push(make_pair(0, StartPoint));
        while (next.empty() == false) {
            pair<ll, int> now = next.top();
            next.pop();
            if (dist[now.second] != now.first) continue;
            for (auto x : vertexs[now.second]) {
                ll now_cost = now.first + Cost_Function(x.second);
                if (dist[x.first] > now_cost) {
                    dist[x.first] = now_cost;
                    next.push(mp(now_cost, x.first));
                }
            }
        }
        return dist;
    }
};

class Dinic {
public:
    struct edge {
        int to;
        int cap;
        int rev;
    };
    vector<vector<edge>> Graph;
    vector<int> level;
    vector<int> itr;
    Dinic(int n) {
        Graph = vector<vector<edge>>(n, vector<edge>());
    }
    void add_edge(int a, int b, int cap) {
        Graph[a].push_back(edge{ b, cap ,(int)Graph[b].size() });
        Graph[b].push_back(edge{ a,0,(int)Graph[a].size() - 1 });
    }
    void bfs(int s) {
        level = vector<int>(Graph.size(), -1);
        level[s] = 0;
        queue<int> next;
        next.push(s);
        while (next.empty() == false) {
            int now = next.front();
            next.pop();
            for (auto x : Graph[now]) {
                if (x.cap == 0) continue;
                if (level[x.to] == -1) {
                    level[x.to] = level[now] + 1;
                    next.push(x.to);
                }
            }
        }
    }
    int dfs(int now, int goal, int val) {
        if (goal == now) return val;
        for (int& i = itr[now]; i < (int)Graph[now].size(); ++i) {
            edge& target = Graph[now][i];
            if (target.cap > 0 && level[now] < level[target.to]) {
                int d = dfs(target.to, goal, min(val, target.cap));
                if (d > 0) {
                    target.cap -= d;
                    Graph[target.to][target.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }
    int run(int s, int t) {
        int ans = 0;
        int f = 0;
        while (bfs(s), level[t] >= 0) {
            itr = vector<int>(Graph.size(), 0);
            while ((f = dfs(s, t, 1e9)) > 0) {
                ans += f;
            }
        }
        return ans;
    }
};

//by ei1333
//https://ei1333.github.io/luzhiled/snippets/structure/segment-tree.html
template< typename Monoid >
struct SegmentTree {
    using F = function< Monoid(Monoid, Monoid) >;

    int sz;
    vector< Monoid > seg;

    const F f;
    const Monoid M1;

    SegmentTree(int n, const F f, const Monoid& M1) : f(f), M1(M1) {
        sz = 1;
        while (sz < n) sz <<= 1;
        seg.assign(2 * sz + 1, M1);
    }

    void set(int k, const Monoid& x) {
        seg[k + sz] = x;
    }

    void build() {
        for (int k = sz - 1; k > 0; k--) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    void update(int k, const Monoid& x) {
        k += sz;
        seg[k] = x;
        while (k >>= 1) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    Monoid query(int a, int b) {
        Monoid L = M1, R = M1;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) L = f(L, seg[a++]);
            if (b & 1) R = f(seg[--b], R);
        }
        return f(L, R);
    }

    Monoid operator[](const int& k) const {
        return seg[k + sz];
    }

    template< typename C >
    int find_subtree(int a, const C& check, Monoid& M, bool type) {
        while (a < sz) {
            Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
            if (check(nxt)) a = 2 * a + type;
            else M = nxt, a = 2 * a + 1 - type;
        }
        return a - sz;
    }


    template< typename C >
    int find_first(int a, const C& check) {
        Monoid L = M1;
        if (a <= 0) {
            if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
            return -1;
        }
        int b = sz;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) {
                Monoid nxt = f(L, seg[a]);
                if (check(nxt)) return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    template< typename C >
    int find_last(int b, const C& check) {
        Monoid R = M1;
        if (b >= sz) {
            if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
            return -1;
        }
        int a = sz;
        for (b += sz; a < b; a >>= 1, b >>= 1) {
            if (b & 1) {
                Monoid nxt = f(seg[--b], R);
                if (check(nxt)) return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }
};

unsigned long xor128() {
    static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    unsigned long t = (x ^ (x << 11));
    x = y; y = z; z = w;
    return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

void init() {
    iostream::sync_with_stdio(false);
    cout << fixed << setprecision(20);
}

#define int long long
void solve() {
    int n;
    cin >> n;
    vector<int> inputs;
    REP(i, n) {
        string s;
        cin >> s;
        if (s == "U") {
            inputs.push_back(0);
        }
        else if (s == "D") {
            inputs.push_back(1);
        }
    }
    vector<vector<modint>> dp(n + 2, vector<modint>(n + 2, modint(0, MAX_MOD)));
    dp[0][0] = modint(1, MAX_MOD);
    for (int i = 0; i < inputs.size(); ++i) {
        for (int q = 0; q <= i; ++q) {
            if (inputs[i] == 1) {
                //down, required to connect.
                dp[i + 1][q + 1] += dp[i][q] * modint(i - q, MAX_MOD);
                dp[i + 1][q + 2] += dp[i][q] * modint(i - q, MAX_MOD) * modint(i - q, MAX_MOD);
            }
            else {

                dp[i + 1][q] += dp[i][q];
                dp[i + 1][q + 1] += dp[i][q] * modint(i - q, MAX_MOD);
            }
        }
    }
    cout << dp[inputs.size()][inputs.size()] << endl;
}

#undef int
int main() {
    init();
    solve();
}
