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
157
158
159
160
161
162
163
164
165
166
167
#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using db = double;
using ull = unsigned long long;
 
using pi = pair<int, int>;
using pl = pair<ll, ll>;
 
using vi = vector<int>;
using vl = vector<ll>;
using vpi = vector<pi>;
using vpl = vector<pl>;
 
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define f first
#define s second
 
#define tcT template<class T
#define tcTU tcT, class U
 
#define sz(x) int((x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep(i,a,b) for(int i = (a); i < (b); i++)
#define rrep(i,a,b) for(int i = (b) - 1; i >= (a); i--)
 
const db PI = acos(-1);
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
 
tcT> bool ckmin(T& a, const T& b) { return b < a ? a=b, 1 : 0; }
tcT> bool ckmax(T& a, const T& b) { return a < b ? a=b, 1 : 0; }
 
tcT> void _dbg(const char *sdbg, T h){ cerr<<sdbg<<'='<<h<<endl; }
tcT, class... TA> void _dbg(const char *sdbg, T h, TA... a) {
	while(*sdbg!=',') cerr<<*sdbg++;
	cerr<<'='<<h<<','; _dbg(sdbg+1, a...);
}
 
tcT> ostream &operator<<(ostream& os, vector<T> V) {
	os << "["; for (auto vv : V) os << vv << ","; return os << "]";
}
tcT, class V> ostream &operator<<(ostream &os, pair<T,V> P) {
	return os << "(" << P.f << "," << P.s << ")";
}
 
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (__VA_ARGS__)
#define cerr if(0)cout
#endif

template<int MOD, int RT> struct mint {
	static const int mod = MOD;
	static constexpr mint rt() { return RT; }
	int v; explicit operator int() const { return v; }
	mint():v(0) {}
	mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD);
		if (v < 0) v += MOD; }
	bool operator==(const mint& o) const {
		return v == o.v; }
	friend bool operator!=(const mint& a, const mint& b) { 
		return !(a == b); }
	friend bool operator<(const mint& a, const mint& b) { 
		return a.v < b.v; }
   
	mint& operator+=(const mint& o) { 
		if ((v += o.v) >= MOD) v -= MOD; 
		return *this; }
	mint& operator-=(const mint& o) { 
		if ((v -= o.v) < 0) v += MOD; 
		return *this; }
	mint& operator*=(const mint& o) { 
		v = int((ll)v*o.v%MOD); return *this; }
	mint& operator/=(const mint& o) { return (*this) *= inv(o); }
	friend mint pow(mint a, ll p) {
		mint ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mint inv(const mint& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mint operator-() const { return mint(-v); }
	mint& operator++() { return *this += 1; }
	mint& operator--() { return *this -= 1; }
	friend mint operator+(mint a, const mint& b) { return a += b; }
	friend mint operator-(mint a, const mint& b) { return a -= b; }
	friend mint operator*(mint a, const mint& b) { return a *= b; }
	friend mint operator/(mint a, const mint& b) { return a /= b; }
};

constexpr int MOD = 1e9+7;

using mi = mint<MOD,5>;
using vmi = vector<mi>;
using pmi = pair<mi,mi>;
using vpmi = vector<pmi>;

ostream& operator<<(ostream &os, mi x) {
	return os << x.v;
}

constexpr int MAXN = 605;

mi dpl[2][MAXN][MAXN];
mi dpr[2][MAXN][MAXN];

string s[MAXN];
int n;

signed main() {
	ios_base::sync_with_stdio(false); cin.tie(nullptr);

	cin >> n;
	rep(i,0,n) cin >> s[i];

	rep(side,0,2) {
		rep(id,0,n) {
			if (side == 1) {
				reverse(all(s[id]));
				rep(i,0,sz(s[id])) {
					s[id][i] = (s[id][i] == 'P' ? 'L' : 'P');
				}
			}

			fill(dpl[side][id], dpl[side][id]+MAXN, 0);
			fill(dpr[side][id], dpr[side][id]+MAXN, 0);

			dpl[side][id][0] = 1;

			rep(i,0,sz(s[id])) {
				if (s[id][i] == 'L') {
					rrep(j,1,i+2) {
						dpl[side][id][j] = dpl[side][id][j-1] + dpr[side][id][j-1];
					}
				}
				else {
					rep(j,0,i+2) {
						dpr[side][id][j] = dpl[side][id][j+1] + dpr[side][id][j+1];
					}
				}
			}
		}
	}

	rep(id1,0,n) {
		rep(id2,0,n) {
			mi res = dpr[0][id1][0];
			res += (dpl[0][id1][0] + dpr[0][id1][0] - dpl[0][id1][1]) * dpr[1][id2][0];

			rep(k,1,sz(s[id1])+1) {
				res += (dpl[0][id1][k] + dpr[0][id1][k] - dpl[0][id1][k+1]) * dpr[1][id2][k];
				res += (dpl[0][id1][k] + dpr[0][id1][k] - dpr[0][id1][k-1]) * dpl[1][id2][k];
			}

			cout << res << " ";
		}

		cout << "\n";
	}

	return 0;
}