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
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
#include<bits/stdc++.h>
using namespace std;
#ifdef LOC
template <class T, class U> auto &operator<<(ostream &out, pair<T, U> a) { return out << "(" << a.first << ", " << a.second << ")"; }
template <class T, class = class enable_if<!is_same<T, string>(), class T::iterator>::type> auto &operator<<(ostream &out, T a) {
    out << "{";
    bool fi = 1;
    for(auto b : a) {
        if(fi) {out<<b; fi=0;}
        else out<<", "<<b;
    }
    return out << "}";
}

template <class T, class X, class Y> auto &operator<<(ostream &out, const priority_queue<T,X,Y>& a) {auto b = a; vector<T> v; while(!b.empty()) {v.push_back(b.top()); b.pop();} return out<<v; }
void dump(){
   cerr << "\e[39m"<<"\n";
}
template <class T, class... Ts> void dump(T a, Ts... x) {
   cerr << a << ", ";
   dump(x...);
}
#define debug(...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<"\t"<<"[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__)
#else
#define debug(...) ;
#endif

#define fwd(i, a, b) for(int i=(a);i<(int)(b);i++)
#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define all(X) (X).begin(), (X).end()
#define sz(X) ((int)(X).size())
#define mp make_pair
#define st first
#define nd second


template <int32_t _MODD>
    struct modint {
    int32_t value;
    modint() = default;
    modint(int32_t value_) : value(value_) {}
    inline modint<_MODD> operator + (modint<_MODD> other) const { int32_t c = this->value + other.value; return modint<_MODD>(c >= _MODD ? c - _MODD : c); }
    inline modint<_MODD> operator - (modint<_MODD> other) const { int32_t c = this->value - other.value; return modint<_MODD>(c <	0 ? c + _MODD : c); }
    inline modint<_MODD> operator * (modint<_MODD> other) const { int32_t c = (int64_t)this->value * other.value % _MODD; return modint<_MODD>(c < 0 ? c + _MODD : c); }
    inline modint<_MODD> & operator += (modint<_MODD> other) { this->value += other.value; if (this->value >= _MODD) this->value -= _MODD; return *this; }
    inline modint<_MODD> & operator -= (modint<_MODD> other) { this->value -= other.value; if (this->value <	0) this->value += _MODD; return *this; }
    inline modint<_MODD> & operator *= (modint<_MODD> other) { this->value = (int64_t)this->value * other.value % _MODD; if (this->value < 0) this->value += _MODD; return *this; }
    inline modint<_MODD> operator - () const { return modint<_MODD>(this->value ? _MODD - this->value : 0); }
    modint<_MODD> pow(uint64_t k) const {
        modint<_MODD> x = *this, y = 1;
        for (; k; k >>= 1) {
        if (k & 1) y *= x;
        x *= x;
        }
        return y;
    }
    modint<_MODD> inv() const { return pow(_MODD - 2); }  // _MODD must be a prime
    inline modint<_MODD> operator /  (modint<_MODD> other) const { return *this *  other.inv(); }
    inline modint<_MODD> operator /= (modint<_MODD> other)	   { return *this *= other.inv(); }
    inline bool operator == (modint<_MODD> other) const { return value == other.value; }
    inline bool operator != (modint<_MODD> other) const { return value != other.value; }
    inline bool operator < (modint<_MODD> other) const { return value < other.value; }
    inline bool operator > (modint<_MODD> other) const { return value > other.value; }
    };
    template <int32_t _MODD> modint<_MODD> operator * (int64_t value, modint<_MODD> n) { return modint<_MODD>(value) * n; }
    template <int32_t _MODD> modint<_MODD> operator * (int32_t value, modint<_MODD> n) { return modint<_MODD>(value % _MODD) * n; }
    template <int32_t _MODD> istream & operator >> (istream & in, modint<_MODD> &n) { return in >> n.value; }
    template <int32_t _MODD> ostream & operator << (ostream & out, modint<_MODD> n) { return out << n.value; }

typedef modint<(int)(1e9+7)> mint;
typedef vector<mint> vm;


struct DPs {
    vm up;
    vm down;
    vm prevLUp;
    vm prevPDown;
};

DPs dp2(const string& s) {
    int n = sz(s);
    vm dpUp(n+1);
    vm dpDown(n+1);
    dpUp[0] = 1;

    vm prevLUp(n+1), prevPDown(n+1);
    fwd(i,1,n+1) {
        if(s[i-1] == 'L') {
            for(int l=sz(dpUp)-1; l>=1; l--)
                dpUp[l] += dpUp[l-1] + dpDown[l-1] - prevLUp[l];
            
            prevLUp = dpUp;
        }
        else {
            for(int l=0; l<sz(dpUp)-1; l++)
                dpDown[l] += dpUp[l+1] + dpDown[l+1] - prevPDown[l];

            prevPDown = dpDown;
        }
    }
    return {dpUp, dpDown, prevLUp, prevPDown};
}

vm unextendible(const DPs& dp, const string& s, char dir) {
    vm res(sz(dp.up));
    rep(i, sz(res))
        res[i] = dp.up[i] + dp.down[i];

    if(count(all(s), dir) > 0) {
        if(dir == 'L')
            rep(i,sz(res)-1)
                res[i] -= dp.prevLUp[i+1];
        else 
            fwd(i,1,sz(res))
                res[i] -= dp.prevPDown[i-1];
    }
    return res;
}

mint solveJoint(const DPs& dpb, const vm& ual, const vm& uap) {
    mint res=0;
    rep(i,min(sz(ual), sz(dpb.down)))
        res += ual[i]*dpb.down[i] + uap[i]*dpb.up[i];
    return res;
}

int32_t main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vector<string> tab(n);
    rep(i,n) {
        cin >> tab[i];
    }
    vector<DPs> dpsInv(n);
    rep(i,n) {
        string cp = tab[i];
        reverse(all(cp));
        for(auto &a:cp)
            a = (a == 'L' ? 'P' : 'L');
        dpsInv[i] = dp2(cp);
    }

    rep(i,n) {
        auto dp = dp2(tab[i]);
        auto uL = unextendible(dp, tab[i], 'L');
        auto uR = unextendible(dp, tab[i], 'P');
        
        rep(j,n)
            cout<<solveJoint(dpsInv[j], uL, uR)-mint(1)<<" ";
        
        cout<<"\n";
    }
}