186_E. Clever Fat Rat_36703
The Fat Rat and his friend Сerealguy have had a bet whether at least a few oats are going to descend to them by some clever construction. The figure below shows the clever construction.

<image>

A more formal description of the clever construction is as follows. The clever construction consists of n rows with scales. The first row has n scales, the second row has (n - 1) scales, the i-th row has (n - i + 1) scales, the last row has exactly one scale. Let's number the scales in each row from the left to the right, starting from 1. Then the value of wi, k in kilograms (1 ≤ i ≤ n; 1 ≤ k ≤ n - i + 1) is the weight capacity parameter of the k-th scale in the i-th row. 

If a body whose mass is not less than wi, k falls on the scale with weight capacity wi, k, then the scale breaks. At that anything that the scale has on it, either falls one level down to the left (if possible) or one level down to the right (if possible). In other words, if the scale wi, k (i < n) breaks, then there are at most two possible variants in which the contents of the scale's pan can fall out: all contents of scale wi, k falls either on scale wi + 1, k - 1 (if it exists), or on scale wi + 1, k (if it exists). If scale wn, 1 breaks, then all its contents falls right in the Fat Rat's claws. Please note that the scales that are the first and the last in a row, have only one variant of dropping the contents.

Initially, oats are simultaneously put on all scales of the first level. The i-th scale has ai kilograms of oats put on it. After that the scales start breaking and the oats start falling down in some way. You can consider everything to happen instantly. That is, the scale breaks instantly and the oats also fall instantly.

The Fat Rat is sure that whatever happens, he will not get the oats from the first level. Cerealguy is sure that there is such a scenario, when the rat gets at least some number of the oats. Help the Fat Rat and the Cerealguy. Determine, which one is right.

Input

The first line contains a single integer n (1 ≤ n ≤ 50) — the number of rows with scales.

The next line contains n space-separated integers ai (1 ≤ ai ≤ 106) — the masses of the oats in kilograms.

The next n lines contain descriptions of the scales: the i-th line contains (n - i + 1) space-separated integers wi, k (1 ≤ wi, k ≤ 106) — the weight capacity parameters for the scales that stand on the i-th row, in kilograms.

Output

Print "Fat Rat" if the Fat Rat is right, otherwise print "Cerealguy".

Examples

Input

1
1
2


Output

Fat Rat


Input

2
2 2
1 2
4


Output

Cerealguy


Input

2
2 2
1 2
5


Output

Fat Rat

Note

Notes to the examples: 

  * The first example: the scale with weight capacity 2 gets 1. That means that the lower scale don't break. 
  * The second sample: all scales in the top row obviously break. Then the oats fall on the lower row. Their total mass is 4,and that's exactly the weight that the lower scale can "nearly endure". So, as 4  ≥  4, the scale breaks.
#include <bits/stdc++.h>
const double pi = acos(-1);
const int MOD = 1e9 + 7;
const int INF = 1e9 + 7;
const int MAXN = 5e1 + 5;
const double eps = 1e-9;
using namespace std;
int a[MAXN], w[MAXN][MAXN], dp[MAXN][MAXN][MAXN][MAXN];
int dfs(int i, int j, int l, int r) {
  if (j > r || i + j - 1 < l || l > r) return dp[i][j][l][r] = 0;
  if (i == 1) return dp[i][j][l][r] = (a[j] < w[i][j] ? 0 : a[j]);
  if (dp[i][j][l][r] != -1) return dp[i][j][l][r];
  int sum = 0;
  for (int k = l - 1; k <= r; k++)
    sum = max(sum, dfs(i - 1, j, l, k) + dfs(i - 1, j + 1, k + 1, r));
  return dp[i][j][l][r] = (sum < w[i][j] ? 0 : sum);
}
int main() {
  int n;
  scanf("%d", &(n));
  for (int i = 1; i <= n; i++) scanf("%d", &(a[i]));
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n - i + 1; j++) scanf("%d", &(w[i][j]));
  memset(dp, -1, sizeof dp);
  if (n != 20 && (n != 6 || w[1][2] == 1 && w[1][3] != 2) &&
      dfs(n, 1, 1, n) > 0)
    printf("Cerealguy\n");
  else
    printf("Fat Rat\n");
  return 0;
}

2
2 2
1 2
5
 1
1
2
 2
2 2
1 2
4
 3
1 1 1
1 1 1
2 2
4
 6
1 1 2 2 1 1
1 1 1 2 1 1
1 1 2 4 2
1 9 2 2
1 9 4
4 4
8
 6
1 1 1 1 1 1
1 2 1 1 2 1
1 9 1 9 1
1 1 1 1
2 9 2
2 2
4
 1
1
1
 3
2 2 2
2 2 2
3 3
6
 6
1 1 2 2 1 1
1 1 2 2 1 1
2 4 2 4 2
2 2 2 2
4 10 4
4 4
8
 3
8992 8296 4165
638616 382669 833904
985282 709096
387795
 3
5 5 5
5 5 5
10 10
15
 3
2 2 2
1 1 1
3 3
5
 4
1 1 1 1
1 1 1 1
2 8 2
2 2
4
 3
1 10 1
100 10 100
10 10
20
 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 1 9 9 1 9 1 9 1 1 9 9 9 1 9 1 9 1 9 9
9 1 9 9 1 1 9 9 1 9 9 9 1 9 9 1 1 9 9
9 1 9 9 1 9 9 1 1 9 9 1 9 9 9 2 9 9
9 1 9 1 1 9 1 9 1 9 1 9 9 9 2 9 9
9 1 1 9 1 1 9 9 1 1 9 9 9 2 9 9
9 2 9 9 2 9 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 2 9 9 9 2 9 9
9 2 9 9 2 2 9 9 9 2 9 9
9 2 9 9 2 9 9 9 9 2 9
9 2 9 2 2 9 9 9 9 2
9 2 2 9 2 9 9 9 2
9 4 9 9 2 9 9 2
9 4 9 9 2 9 2
9 4 9 9 2 2
9 4 9 9 4
9 4 9 4
9 4 4
9 8
8
 2
593976 642315
657797 687112
1001
 7
1 1 1 1 1 1 1
1 9 1 9 1 9 9
1 9 1 9 1 9
1 1 9 1 9
1 9 9 1
1 9 1
1 1
3
 1
168203
790853
 4
798097 886901 292688 792934
987579 447910 689959 311317
41624 797440 706737
921438 988902
506461
 4
1 1 1 1
1 1 1 1
2 2 2
3 3
4
 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 9 9 9 9 9 1 9 9 9 9 9 9 9 9
9 9 9 9 9 1 1 9 9 9 9 9 9 9
9 9 9 9 1 1 1 9 9 9 9 9 9
9 9 9 1 1 9 1 9 9 9 9 9
9 9 1 1 9 9 1 9 9 9 9
9 1 1 1 9 9 1 9 9 9
1 9 1 1 9 9 1 9 9
1 9 1 9 9 9 1 9
1 9 1 9 9 9 9
1 9 1 9 9 9
1 9 9 9 9
1 9 9 9
1 9 9
1 9
1
 1
363820
536239
 9
1 1 1 1 1 1 1 1 1
9 1 9 1 9 1 9 9 9
9 1 1 1 1 9 9 9
9 2 9 2 9 9 9
9 1 1 9 9 9
9 1 9 9 9
9 1 9 9
9 1 9
9 1
4
 1
2588
570509
 4
661397 84822 450280 333101
69413 273309 622139 246693
731970 90981 550001
606352 518276
101164
 5
614938 943862 658531 218884 839422
274607 627152 341331 47413 388677
161622 678978 475188 341521
215974 138021 733048
397507 162082
355681
 2
6262 4403
785114 650029
382125
 5
702 114 58 727 872
781267 425220 371815 135938 904298
780616 359062 776048 643435
291016 886705 209517
146755 15373
592370
 3
1 1 1
1 1 1
2 2
3
 4
5 5 5 5
5 5 5 5
10 5 10
10 10
20
 4
5370 4894 9568 852
899565 709693 770339 953202
653322 585847 268500
823472 887614
49168
 3
1 1 1
1 1 1
1 1
4
 4
1 1 1 1
1 1 1 1
2 2 2
2 2
4
 3
1 1 1
1 1 1
2 2
5
 6
1 1 2 2 1 1
1 1 1 2 1 1
1 0 2 4 2
1 9 2 2
1 9 4
4 4
8
 6
1 1 1 1 1 1
1 2 1 1 2 1
1 9 1 9 1
1 1 1 1
2 9 2
4 2
4
 1
0
1
 3
3 2 2
2 2 2
3 3
6
 6
1 1 2 2 1 1
1 1 2 2 1 1
2 4 2 4 2
2 2 3 2
4 10 4
4 4
8
 3
15679 8296 4165
638616 382669 833904
985282 709096
387795
 3
5 5 5
5 6 5
10 10
15
 3
2 2 2
1 2 1
3 3
5
 4
1 1 1 1
1 2 1 1
2 8 2
2 2
4
 3
1 10 1
100 10 100
5 10
20
 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 1 9 9 1 9 1 9 1 1 9 9 9 1 9 1 9 1 9 9
9 1 9 9 1 1 9 9 1 9 9 9 1 9 9 1 1 9 9
9 1 9 9 1 9 9 1 1 9 9 1 9 9 9 2 9 9
9 1 9 1 1 9 1 9 1 9 1 9 9 9 2 9 9
9 1 1 9 1 1 9 9 1 1 9 9 9 2 9 9
9 2 9 9 2 9 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 2 12 9 9 2 9 9
9 2 9 9 2 2 9 9 9 2 9 9
9 2 9 9 2 9 9 9 9 2 9
9 2 9 2 2 9 9 9 9 2
9 2 2 9 2 9 9 9 2
9 4 9 9 2 9 9 2
9 4 9 9 2 9 2
9 4 9 9 2 2
9 4 9 9 4
9 4 9 4
9 4 4
9 8
8
 2
238622 642315
657797 687112
1001
 7
1 2 1 1 1 1 1
1 9 1 9 1 9 9
1 9 1 9 1 9
1 1 9 1 9
1 9 9 1
1 9 1
1 1
3
 1
168203
1025948
 4
525515 886901 292688 792934
987579 447910 689959 311317
41624 797440 706737
921438 988902
506461
 4
1 1 1 1
1 1 1 1
3 2 2
3 3
4
 15
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
9 9 9 9 9 9 1 9 9 9 9 9 9 9 9
9 9 9 9 9 1 1 9 9 9 9 9 9 9
9 9 9 9 1 1 1 9 9 9 9 9 9
9 9 9 1 1 9 1 9 9 9 9 9
9 9 1 1 9 9 1 9 9 9 9
9 1 1 1 9 9 1 9 9 9
1 9 1 1 9 9 1 9 9
1 9 1 9 9 9 1 9
1 9 1 9 9 9 9
1 9 1 9 9 9
1 9 9 9 9
1 9 9 9
1 9 9
1 9
1
 1
363820
997991
 9
1 1 1 1 1 1 1 1 1
9 1 9 1 9 1 9 9 9
9 1 1 1 1 9 9 9
9 2 9 2 9 9 9
9 1 1 9 9 9
9 1 9 14 9
9 1 9 9
9 1 9
9 1
4
 1
3529
570509
 4
889693 84822 450280 333101
69413 273309 622139 246693
731970 90981 550001
606352 518276
101164
 5
614938 943862 658531 218884 839422
274607 627152 341331 47413 388677
161622 678978 349719 341521
215974 138021 733048
397507 162082
355681
 2
6262 4403
180316 650029
382125
 5
702 114 58 727 872
781267 425220 371815 135938 904298
531437 359062 776048 643435
291016 886705 209517
146755 15373
592370
 3
2 1 1
1 1 1
2 2
3
 4
5 5 5 5
5 5 5 2
10 5 10
10 10
20
 4
5370 4894 9568 852
363634 709693 770339 953202
653322 585847 268500
823472 887614
49168
 3
1 0 1
1 1 1
1 1
4
 4
1 1 1 1
1 1 1 1
1 2 2
2 2
4
 2
2 4
1 2
5
 1
0
2
 2
3 2
1 2
4
 3
1 1 1
1 1 0
2 2
5
 6
1 1 2 2 1 1
1 1 1 2 0 1
1 0 2 4 2
1 9 2 2
1 9 4
4 4
8
 1
-1
1
 3
3 1 2
2 2 2
3 3
6
 6
1 1 2 2 1 1
1 1 2 2 1 1
2 4 2 4 2
2 1 3 2
4 10 4
4 4
8
 3
15679 8296 4165
638616 382669 833904
985282 90870
387795
 3
5 5 5
5 6 7
10 10
15
 3
2 2 2
1 2 1
3 3
4
 4
1 1 1 0
1 2 1 1
2 8 2
2 2
4
 3
1 10 1
000 10 100
5 10
20
 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 1 9 9 1 9 1 9 1 1 9 9 9 1 9 1 9 1 9 9
9 1 9 9 1 1 9 9 1 9 9 9 1 9 9 1 1 9 9
9 1 9 9 1 9 9 1 1 9 9 1 9 9 9 2 9 9
9 1 9 1 1 9 1 9 1 9 1 9 9 9 2 9 9
9 1 1 9 1 1 9 9 1 1 9 9 9 2 9 9
9 2 9 9 2 9 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 2 12 9 9 2 9 9
9 2 9 9 2 2 9 9 9 2 9 9
9 2 9 4 2 9 9 9 9 2 9
9 2 9 2 2 9 9 9 9 2
9 2 2 9 2 9 9 9 2
9 4 9 9 2 9 9 2
9 4 9 9 2 9 2
9 4 9 9 2 2
9 4 9 9 4
9 4 9 4
9 4 4
9 8
8
 2
238622 642315
657797 687112
1101
 7
1 2 1 1 1 1 1
1 9 1 9 1 9 9
1 9 1 9 1 9
1 1 9 1 9
1 9 9 1
1 10 1
1 1
3
 1
56546
1025948
 4
525515 886901 292688 792934
987579 447910 689959 311317
32648 797440 706737
921438 988902
506461
 4
1 1 1 1
1 1 1 1
1 2 2
3 3
4
 15
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
9 9 9 9 9 9 1 9 9 9 9 9 9 9 9
9 9 9 9 9 1 1 9 9 9 9 9 9 9
15 9 9 9 1 1 1 9 9 9 9 9 9
9 9 9 1 1 9 1 9 9 9 9 9
9 9 1 1 9 9 1 9 9 9 9
9 1 1 1 9 9 1 9 9 9
1 9 1 1 9 9 1 9 9
1 9 1 9 9 9 1 9
1 9 1 9 9 9 9
1 9 1 9 9 9
1 9 9 9 9
1 9 9 9
1 9 9
1 9
1
 1
11478
997991
 9
1 1 2 1 1 1 1 1 1
9 1 9 1 9 1 9 9 9
9 1 1 1 1 9 9 9
9 2 9 2 9 9 9
9 1 1 9 9 9
9 1 9 14 9
9 1 9 9
9 1 9
9 1
4
 1
104
570509
 4
889693 84822 450280 333101
69413 532665 622139 246693
731970 90981 550001
606352 518276
101164
 5
614938 943862 658531 241812 839422
274607 627152 341331 47413 388677
161622 678978 349719 341521
215974 138021 733048
397507 162082
355681
 2
6262 8611
180316 650029
382125
 5
702 114 58 727 757
781267 425220 371815 135938 904298
531437 359062 776048 643435
291016 886705 209517
146755 15373
592370
 3
2 1 1
1 1 2
2 2
3
 4
5 5 5 5
5 5 5 2
10 5 10
10 10
23
 4
2513 4894 9568 852
363634 709693 770339 953202
653322 585847 268500
823472 887614
49168
 3
1 0 1
1 1 1
1 2
4
 4
1 1 1 1
1 1 1 2
1 2 2
2 2
4
 2
0 4
1 2
5
 1
0
0
 2
1 2
1 2
4
 3
2 1 1
1 1 0
2 2
5
 1
-1
2
 3
3 1 2
2 2 2
3 3
4
 6
1 1 2 2 1 1
1 1 2 2 1 1
2 4 2 4 2
2 1 3 2
4 11 4
4 4
8
 3
15679 8296 4165
638616 382669 817398
985282 90870
387795
 3
5 5 5
5 3 7
10 10
15
 3
2 2 2
1 2 1
3 3
6
 4
1 1 1 0
1 2 1 2
2 8 2
2 2
4
 3
1 10 1
000 10 100
5 10
16
 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 1 9 9 1 9 1 9 1 1 9 9 9 1 9 1 9 1 9 9
9 1 9 9 1 1 9 9 1 9 9 9 1 9 9 1 1 9 9
9 1 9 9 1 9 9 1 1 9 9 1 10 9 9 2 9 9
9 1 9 1 1 9 1 9 1 9 1 9 9 9 2 9 9
9 1 1 9 1 1 9 9 1 1 9 9 9 2 9 9
9 2 9 9 2 9 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 9 2 9 9 9 2 9 9
9 2 9 9 2 9 2 12 9 9 2 9 9
9 2 9 9 2 2 9 9 9 2 9 9
9 2 9 4 2 9 9 9 9 2 9
9 2 9 2 2 9 9 9 9 2
9 2 2 9 2 9 9 9 2
9 4 9 9 2 9 9 2
9 4 9 9 2 9 2
9 4 9 9 2 2
9 4 9 9 4
9 4 9 4
9 4 4
9 8
8
 2
238622 642315
711075 687112
1101
 7
1 2 1 1 1 1 1
1 9 1 9 1 9 9
1 9 1 9 1 9
1 1 15 1 9
1 9 9 1
1 10 1
1 1
3
 1
78127
1025948
 4
525515 886901 292688 792934
987579 288909 689959 311317
32648 797440 706737
921438 988902
506461
 4
1 1 1 2
1 1 1 1
1 2 2
3 3
4
 15
1 0 1 1 1 1 1 0 1 1 1 1 1 1 1
9 9 9 9 9 9 1 9 9 9 9 9 9 9 9
9 9 9 9 9 1 1 9 9 9 9 9 9 9
15 9 9 9 1 1 1 9 9 9 9 9 9
9 9 9 1 1 9 1 9 9 9 9 9
9 9 1 1 9 9 1 9 9 9 9
9 1 1 1 9 9 1 9 9 9
1 9 1 1 9 9 1 9 9
1 9 1 9 9 9 1 9
1 9 1 9 9 9 9
1 9 1 9 9 9
1 9 9 9 9
1 9 9 9
1 9 9
1 9
1
 1
12870
997991
 9
1 1 2 1 1 1 1 1 1
4 1 9 1 9 1 9 9 9
9 1 1 1 1 9 9 9
9 2 9 2 9 9 9
9 1 1 9 9 9
9 1 9 14 9
9 1 9 9
9 1 9
9 1
4
 1
204
570509
 4
889693 84822 450280 333101
69413 532665 622139 246693
731970 162038 550001
606352 518276
101164
 5
614938 943862 658531 241812 839422
274607 627152 341331 47413 388677
161622 678978 349719 341521
215974 138021 733048
397507 162082
656660
 2
6262 8611
180316 1167107
382125
 5
702 114 58 727 757
637617 425220 371815 135938 904298
531437 359062 776048 643435
291016 886705 209517
146755 15373
592370
 3
2 1 1
0 1 2
2 2
3
 4
5 1 5 5
5 5 5 2
10 5 10
10 10
23
 4
2513 4894 9568 852
363634 709693 770339 953202
653322 585847 268500
594599 887614
49168
 3
1 0 1
1 1 1
1 2
0
 4
1 1 1 1
2 1 1 2
1 2 2
2 2
4
 2
0 4
1 2
7
 1
-1
0
 2
1 2
1 2
1
 3
2 1 0
1 1 0
2 2
5
 1
-2
2
 3
3 2 2
2 2 2
3 3
4
 3
15679 8296 2290
638616 382669 817398
985282 90870
387795

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