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
#include <bits/stdc++.h>
#include <unistd.h>
using namespace std;

constexpr int MOD = 1'000'000'007;

static inline void add(int& a, const int b) {
	a += b;
	if (a >= MOD) {
		a -= MOD;
	}
}

constexpr int MAXN = 607;

string s[MAXN];
int sz[MAXN];
int cntL[MAXN], cntP[MAXN];

int dp[MAXN][MAXN][8]; // pref, sum, bitmask(last, canL, canP)
int last_row[2][MAXN][MAXN][8];

void clear(int id) {
	for (int i = 0; i <= sz[id]; i++) {
		for (int sum = 0; sum <= i; sum++) {
			for (int bitmask = 0; bitmask < 8; bitmask++) {
				dp[i][sum][bitmask] = 0;
			}
		}
	}
}

void calc(int id) {
	for (int rep = 0; rep < 2; rep++) {
		clear(id);
		
		dp[0][0][2] = 1;
		int max_sum = 0;
		for (int i = 0; i < sz[id]; i++) {
			if (s[id][i] == 'L') {
				for (int bitmask = 0; bitmask < 8; bitmask++) {
					for (int sum = 0; sum <= max_sum; sum++) {
						add(dp[i + 1][sum][bitmask & 5], dp[i][sum][bitmask]);
					}
					if (bitmask & 2) { // if (canL)
						for (int sum = 0; sum <= max_sum; sum++) {
							add(dp[i + 1][sum + 1][3], dp[i][sum][bitmask]);
						}
					}
				}
				max_sum++;
			}
			else {
				for (int bitmask = 0; bitmask < 8; bitmask++) {
					for (int sum = 0; sum <= max_sum; sum++) {
						add(dp[i + 1][sum][bitmask & 6], dp[i][sum][bitmask]);
					}
					if (bitmask & 1) { // if (canP && sum > 0)
						for (int sum = 1; sum <= max_sum; sum++) {
							add(dp[i + 1][sum - 1][7], dp[i][sum][bitmask]);
						}
					}
				}
			}
		}
		
		if (rep == 0) {
			for (int sum = 0; sum <= sz[id]; sum++) {
				for (int bitmask = 0; bitmask < 8; bitmask++) {
					last_row[rep][id][sum][bitmask] = dp[sz[id]][sum][bitmask];
				}
			}
			reverse(s[id].begin(), s[id].end());
			for (int i = 0; i < sz[id]; i++) {
				if (s[id][i] == 'L') {
					s[id][i] = 'P';
				}
				else {
					s[id][i] = 'L';
				}
			}
		}
		else {
			for (int sum = 0; sum <= sz[id]; sum++) {
				for (int bitmask = 0; bitmask < 8; bitmask++) {
					int new_bitmask = bitmask ^ 7;
					if ((bitmask & 1) != (bitmask >> 1 & 1)) {
						new_bitmask ^= 3;
					}
					last_row[rep][id][sum][new_bitmask] = dp[sz[id]][sum][bitmask];
				}
			}
		}
	}
}

int result[MAXN][MAXN];

char bufor[MAXN * MAXN * 13];
int bufor_last = 0;

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int n;
	cin >> n;
	// n = 600;
	for (int i = 0; i < n; i++) {
		cin >> s[i];
		// for (int j = 0; j < 600; j++) {
			// if (rand() % 2 == 0) {
				// s[i] += 'L';
			// }
			// else {
				// s[i] += 'P';
			// }
		// }
		sz[i] = s[i].size();
		for (int j = 0; j < sz[i]; j++) {
			if (s[i][j] == 'L') {
				cntL[i]++;
			}
			else {
				cntP[i]++;
			}
		}
	}
	
	for (int i = 0; i < n; i++) {
		calc(i);
	}
	
	int tmp;
	int sum;
	long long totalL, totalP, chuj1, chuj2;
	for (int i = n - 1; i >= 0; i--) {
		for (int j = n - 1; j >= 0; j--) {
			tmp = 0;
			sum = 0;
			totalL = ((long long) last_row[1][j][sum][0] + last_row[1][j][sum][1] + last_row[1][j][sum][2] + last_row[1][j][sum][3]) % MOD;
			add(tmp, ((last_row[0][i][sum][6] + last_row[0][i][sum][7]) * totalL) % MOD);
			add(tmp, ((long long) last_row[0][i][sum][4] + last_row[0][i][sum][5] + last_row[0][i][sum][6] + last_row[0][i][sum][7]) % MOD);
			if (cntL[i] == 0) {
				add(tmp, totalL);
			}
			int bound = min(cntL[i], cntP[j]);
			for (sum = 1; sum <= bound; sum++) {
				totalL = ((long long) last_row[1][j][sum][0] + last_row[1][j][sum][1] + last_row[1][j][sum][2] + last_row[1][j][sum][3]) % MOD;
				totalP = ((long long) last_row[1][j][sum][4] + last_row[1][j][sum][5] + last_row[1][j][sum][6] + last_row[1][j][sum][7]) % MOD;
				chuj1 = ((long long) last_row[0][i][sum][2] + last_row[0][i][sum][3] + last_row[0][i][sum][6] + last_row[0][i][sum][7]) % MOD;
				chuj2 = ((long long) last_row[0][i][sum][1] + last_row[0][i][sum][3] + last_row[0][i][sum][5] + last_row[0][i][sum][7]) % MOD;
				add(tmp, (chuj1 * totalL) % MOD);
				add(tmp, (chuj2 * totalP) % MOD);
			}
			result[i][j] = tmp;
		}
	}
	
	for (int i = n - 1; i >= 0; i--) {
		bufor[bufor_last++] = '\n';
		for (int j = n - 1; j >= 0; j--) {
			bufor[bufor_last++] = ' ';
			int tmp = result[i][j];
			do {
				bufor[bufor_last++] = (tmp % 10 + '0');
				tmp /= 10;
			} while (tmp > 0);
		}
	}
	
	// cerr << bufor_last << '\n';
	reverse(bufor, bufor + bufor_last);
	write(1, bufor, bufor_last);
	
	return 0;
}