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
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
//Konrad Paluszek,University of Warsaw(former XIV LO Staszic)
//#STAY AT HOME
#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#define TIME (chrono::steady_clock::now().time_since_epoch().count())
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define xfm(a,b)a##b
#define xwb(a,b)xfm(a,b)
#define _ xwb(nvj,__LINE__)
#define __ xwb(kjy,__LINE__)
#define ___ xwb(cjm,__LINE__)
#define REP(i,n)for(urs(n)i=0;i<(n);++i)
#define PER(r...)for(bool _=1;_||next_permutation(r);_=false)
#define FS(r)r.first,r.second
#define ALL(r)(r).begin(),(r).end()
#define M0(r) memset(r,0,sizeof(r))
#define sim template<class c
#define forbits(i,m)if(m)for(urs(m)i=ctz(m),i##nvj=m;i##nvj;i##nvj^=((urs(m))1<<i),i=i##nvj?ctz(i##nvj):0)
#define fordbits(i,m)if(m)for(urs(m)i=8*sizeof(m)-clz(m)-1,i##nxd=m;i##nxd;i##nxd^=((urs(m))1<<i),i=i##nxd?8*sizeof(m)-clz(i##nxd)-1:0)
#define ksets(t, m, k, n)for(t m=(((t)1<<(k))-1);m<((t)1<<(n));m=nux(m))
#define urs(r...)typename decay<decltype(r)>::type
#define hur(f,g)sim>int f(c a){if(sizeof(c)==8)return g##ll(a);return g(a);}
using namespace __gnu_pbds;using namespace std;using ll=long long;using ld=long double;using ull=unsigned long long;using vi=vector<int>;using vll=vector<ll>;using pii=pair<int,int>;using pll=pair<ll,ll>;using vpii=vector<pii>;using unt=unsigned int;sim>using min_queue=priority_queue<c,vector<c>,greater<>>;sim,class b,class cmp=less<c>>using ordered_map=tree<c,b,cmp,rb_tree_tag,tree_order_statistics_node_update>;sim,class cmp=less<c>>using ordered_set=ordered_map<c,null_type,cmp>;hur(popc,__builtin_popcount)hur(ctz,__builtin_ctz)hur(clz,__builtin_clz)sim,class N>bool mini(c&o,const N&h){if(o>h)return o=h,1;return 0;}sim,class N>bool maxi(c&o,const N&h){if(o<h)return o=h,1;return 0;}
#ifdef LOCAL
#include </home/konrad/cp/headers/debuglib.hpp>
#else
#define loc(...)
#define onl(r...)r
#define debug(...)
#define print_stack(...)
#define mark_stack(...)
#define set_pre(...)
#define reg_it(...)
#define def_op(...) struct _{};
#define mask_set(...)
#define exit my_exit
void __resources();
void my_exit(int x) {cout.flush();
#ifdef LOCAL2
__resources();
#endif
_Exit(x);}
#endif
#define next nexT
#define prev preV
#define tree trEE
#define left lefT
#define right righT
#define div diV
#define y1 y_1
#define pow don't'
ull mix(ull o){o+=0x9e3779b97f4a7c15;o=(o^(o>>30))*0xbf58476d1ce4e5b9;o=(o^(o>>27))*0x94d049bb133111eb;return o^(o>>31);}ull SALT=0x7a14a4b0881ebf9,tqu=0x7a14a4b0881ebf9;ull my_rand(){return tqu=mix(tqu);}void my_srand(ull x){SALT=tqu=x;}const int inf=1023400000;const ll llinf=1234567890000000000ll;ll fix(ll o, ll m){o%=m;if(o<0)o+=m;return o;}
#define rand my_rand
#define srand my_srand
#define random_shuffle(r...)random_shuffle(r,[](int _){return my_rand()%_;})
sim>inline c nux(c m){if(!m)return numeric_limits<c>::max();c A=m&-m;c B=~((A-1)^m);c C=B&-B;c D=(C>>(1+ctz(A)))-1;return C|(m&~(C-1))|D;}sim>void unq(c&x){x.resize(unique(ALL(x))-x.begin());}
//#STAY AT HOME
const int mod = 1e9 + 7;
struct pref_res {
	ll full;
	vector <ll> aft_plus, aft_minus;
	pref_res() : full(), aft_plus(), aft_minus() {}
};
struct suf_res {
	vector <ll> with_plus, with_minus;
};
#define show(f) #f " = " << x.f << "; "
loc (
	ostream &operator<<(ostream &o, const pref_res &x) {
		return o << "[" show(full) show(aft_plus) show(aft_minus) << "]";
	}
	ostream &operator<<(ostream &o, const suf_res &x) {
		return o;
	}
)
void add(ll &a, ll b) {
	a += b;
	if (a >= mod) a -= mod;
}
void add_pro(ll &a, ll b, ll c) {
	(a += b * c) %= mod;
}
const char PLUS = 'L', MINUS = 'P';
vector <vll> calc_dp(const string &s) {
	int n = s.size();
	vector <vll> dp(n + 1, vll(n + 1));
	dp[0][0] = 1;
	vi next_plus(n + 1, -1), next_minus(n + 1, -1);
	for (int i = n - 1; i >= 0; --i) {
		next_plus[i] = next_plus[i + 1];
		next_minus[i] = next_minus[i + 1];
		if (s[i] == PLUS) next_plus[i] = i + 1;
		else next_minus[i] = i + 1;
	}
	REP(i, n) {
		debug(arr(dp, i));
		auto serve = [&](int to, int delta) {
			if (to == -1) return;
			for (int curr_bal = 0; curr_bal <= i; ++curr_bal) {
				int would = curr_bal + delta;
				if (would >= 0) {
					add(dp[to][would], dp[i][curr_bal]);
				}
			}
		};
		serve(next_plus[i], +1);
		serve(next_minus[i], -1);
	}
	return dp;
}
pref_res solve_pref(const string &s) {
	debug(imie(s));
	pref_res r;
	int n = s.size();
	int last_plus = -1, last_minus = -1;
	auto dp = calc_dp(s);
	REP(i, n) {
		if (s[i] == PLUS) last_plus = i;
		else last_minus = i;
	}
	REP(i, n + 1) add(r.full, dp[i][0]);
	r.aft_plus.resize(n + 1);
	r.aft_minus.resize(n + 1);
	REP(b, n + 1) {
		REP(i, n + 1) {
			if (i > last_plus) add(r.aft_plus[b], dp[i][b]);
			if (i > last_minus) add(r.aft_minus[b], dp[i][b]);
		}
	}
	debug(arr(dp, n));
	return r;
}
suf_res solve_suf(string s) {
	suf_res r;
	int n = s.size();
	reverse(ALL(s));
	for (char &x : s) x ^= PLUS ^ MINUS;
	auto dp = calc_dp(s);
	r.with_plus.resize(n + 1);
	r.with_minus.resize(n + 1);
	for (int bal = 0; bal <= n; ++bal) {
		REP(i, n) {
			if (s[i] == PLUS) add(r.with_minus[bal], dp[i + 1][bal]);
			else add(r.with_plus[bal], dp[i + 1][bal]);
		}
	}
	return r;
}
ll extract(const pref_res &pref, const suf_res &suf) {
	ll ans = pref.full;
	REP(i, min(pref.aft_plus.size(), suf.with_plus.size())) {
		add_pro(ans, pref.aft_plus[i], suf.with_plus[i]);
	}
	REP(i, min(pref.aft_minus.size(), suf.with_minus.size())) {
		add_pro(ans, pref.aft_minus[i], suf.with_minus[i]);
	}
	return fix(ans - 1, mod);
}
void solve() {
	int n;
	cin >> n;
	vector <string> a(n);
	for (auto &x : a) cin >> x;
	vector <pref_res> prefs;
	vector <suf_res> sufs;
	for (auto &s : a) {
		prefs.push_back(solve_pref(s));
		debug(imie(s), prefs.back());
	}
	for (auto &s : a) {
		sufs.push_back(solve_suf(s));
		debug(imie(s), sufs.back());
	}
	REP(i, n) {
		REP(j, n) cout << extract(prefs[i], sufs[j]) << " ";
		cout << "\n";
	}
}
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	// unt seed = TIME; debug(imie(seed));srand(seed);
	int t = 1;
	// scanf("%d", &t);
	REP(_, t) solve();
	exit(0);
}
//#STAY AT HOME