10564 - Paths through the Hourglass

[Larry]

Read up on dynamic programming, and you'll see. Basically, it's a way of caching values so that you don't keep on computing the same values. You can look at it as trying all possible paths, but ifyou know the answer at the current "node", then you just return what you stored already instead.

[jpfarias]

Ok, solved!! I just did not think enough before...

I've created a 20x40x351 matrix to store parcial values...

But, how do I solve this with < 0.09 sec with 64k of memory?

JP.

[Yarin]

The memory info is not always correct. If the program executes fast enough, it will always say your program used 64k even though that's not the case (my solution uses ~3 MB memory and is currently the first one on the ranklist). As for speed, I use memoization (not DP) + build the way on the fly. Memoization is probably better than DP because the big array can be quite sparse.

[sohel]

I got this program ac..
and it took 0.619 to get AC( not that bad) .

I would like to know whether everyone used methods similar to mine..

I actually turned over the hourglass and then applied dp..
.. otherwise it becomes very difficult to find the smallest string..

.. is this the method that everyone used.

[ImLazy]

Code: Select all

11 119
8 9 2 7 9 5 4 3 1 2 3
3 4 1 1 3 8 7 4 2 7
7 9 3 1 9 8 6 5 0
2 8 6 0 2 4 8 6
5 0 9 0 0 6 1
3 8 9 3 4 4
6 0 6 6 1
8 4 9 6
3 7 8
8 2
9
1 3
5 9 8
4 0 7 6
3 6 1 5 4
2 0 9 7 3 7
2 6 0 1 6 5 7
5 4 1 2 0 0 1 4
6 0 7 1 7 7 7 7 3
3 5 9 9 8 1 8 2 6 6
0 3 8 0 1 2 5 0 9 4 7

16 145
1 0 8 1 0 9 2 4 9 1 5 7 3 3 4 2
2 0 1 2 7 7 0 2 4 1 0 3 7 3 9
5 9 7 2 0 2 8 6 7 0 8 1 8 3
0 3 6 2 0 2 8 4 1 8 3 7 5
8 1 7 0 4 8 8 1 3 6 7 8
9 5 5 5 6 6 3 0 0 8 8
2 3 0 6 5 0 9 7 2 2
8 2 9 4 4 8 2 7 2
5 8 4 7 3 9 5 1
9 0 2 8 3 1 4
3 1 0 4 0 7
9 0 8 1 4
0 7 9 5
3 8 2
3 2
1
0 4
0 7 5
9 0 5 1
2 0 9 8 9
1 7 3 3 0 7
6 6 0 2 8 9 8
9 9 9 4 2 0 8 7
8 7 3 0 7 6 4 2 1
9 1 6 0 3 3 6 2 2 1
4 3 2 6 0 5 4 9 6 0 8
2 7 4 0 7 6 0 1 2 9 3 8
5 1 5 6 6 8 8 9 8 7 0 7 9
1 5 8 6 3 9 4 5 3 8 2 3 9 4
8 5 1 3 2 8 1 6 4 6 7 7 9 6 4
1 9 2 6 3 1 5 9 7 0 2 6 1 7 6 2

19 272
3 0 2 7 7 7 0 2 0 0 8 6 4 5 0 1 5 7 3
2 7 9 1 1 4 0 3 3 1 5 8 3 0 5 1 0 2
5 1 0 4 0 6 4 8 9 5 6 2 2 2 1 7 4
7 8 6 0 0 2 1 3 9 2 4 1 5 4 0 6
6 8 1 3 3 1 0 5 8 9 3 8 9 8 4
3 9 9 6 9 7 7 2 5 2 3 2 8 3
3 8 5 7 8 8 1 3 5 1 2 0 8
6 5 5 3 9 5 3 5 4 8 5 0
3 5 0 8 4 3 5 8 1 2 6
0 2 2 1 6 5 0 1 7 7
3 8 3 5 1 3 2 1 9
4 2 3 0 1 4 8 6
6 1 3 8 7 9 4
4 3 5 4 4 2
7 7 5 6 6
9 0 7 0
9 8 6
7 3
2
0 1
5 3 5
6 5 4 6
8 1 5 8 5
3 3 2 8 7 6
9 6 4 6 3 2 1
0 5 8 7 0 0 3 7
3 4 6 2 0 1 1 6 5
3 4 9 5 3 4 3 7 7 0
9 1 5 4 0 0 7 1 2 3 7
7 3 3 3 9 1 5 8 8 8 0 2
4 4 3 3 6 7 6 6 1 4 8 1 6
5 9 6 8 7 1 9 1 6 7 6 3 7 1
2 7 9 4 7 1 8 2 4 8 8 1 6 2 0
4 8 5 9 4 4 4 9 9 4 5 3 2 1 7 4
3 1 9 0 7 3 8 4 2 6 9 8 7 7 4 8 7
8 3 2 1 9 3 7 4 4 4 3 5 1 3 2 8 0 9
0 3 4 9 4 4 3 9 8 5 3 8 1 2 3 8 9 8 5

20 240
6 1 8 1 8 7 7 2 8 2 3 6 6 9 6 5 1 3 8 0
7 6 1 6 0 3 1 0 4 3 1 5 8 9 5 4 5 7 4
4 6 7 7 5 2 6 8 8 9 1 9 8 0 5 0 2 9
6 0 2 2 9 2 6 7 3 6 0 5 2 1 7 1 1
5 3 2 6 6 8 1 5 8 6 9 4 6 6 2 8
8 1 6 8 7 8 9 7 9 0 5 8 2 6 9
7 1 7 5 1 6 4 4 9 9 6 1 5 5
6 0 7 5 0 7 9 5 6 8 5 3 7
0 7 5 2 3 0 4 9 8 5 8 0
0 9 7 7 4 4 7 5 9 2 3
2 2 3 1 9 7 3 0 4 3
7 8 0 8 8 1 2 7 4
9 1 9 3 6 2 0 7
2 0 0 5 3 5 7
7 4 4 3 3 8
6 4 4 5 9
2 4 4 2
4 2 5
3 2
3
4 0
2 3 7
2 0 7 7
6 1 7 5 6
7 9 0 8 5 7
4 2 5 6 5 8 8
2 8 5 2 7 6 7 3
3 5 6 9 4 4 5 9 6
9 2 9 5 6 1 7 8 3 7
2 6 9 1 0 0 4 5 6 3 6
4 6 7 6 3 9 1 4 7 5 0 0
5 5 8 8 6 9 8 1 5 6 0 6 0
4 7 8 6 4 0 3 4 1 0 0 4 3 6
1 0 5 6 8 6 7 6 7 8 9 4 5 1 0
2 8 6 7 0 7 7 4 6 2 2 9 6 5 6 4
0 6 9 6 2 9 1 2 6 4 7 0 8 2 4 1 0
0 3 6 1 7 9 8 0 2 9 8 9 7 4 7 7 5 3
9 1 2 9 6 1 1 4 9 8 6 9 7 4 8 2 5 8 2
5 6 1 9 3 7 1 3 2 0 6 8 9 9 3 9 1 1 3 4

3 42
4 9 1
4 3
9
4 9
5 2 1

12 149
2 5 1 8 0 7 5 7 4 2 9 1
8 4 4 8 1 2 8 4 6 7 3
1 5 8 5 4 2 6 6 4 6
1 4 0 4 6 6 7 5 8
1 1 5 1 1 9 0 7
6 3 4 4 5 7 2
6 5 6 2 9 6
5 3 2 1 6
3 4 9 0
5 6 5
0 6
5
3 3
2 6 6
0 6 2 0
0 5 2 0 5
6 1 0 4 9 4
0 2 6 6 4 0 7
2 6 6 8 5 1 0 0
2 1 3 8 4 3 5 0 8
7 0 5 3 5 6 3 0 2 9
9 3 7 9 3 9 3 0 2 5 1
1 8 3 3 7 4 6 7 1 9 4 6

20 242
8 2 5 7 7 8 4 2 0 6 5 0 5 6 0 7 2 4 4 4
0 5 0 6 6 2 6 3 1 7 5 5 5 4 8 9 9 8 1
2 7 7 9 2 1 8 2 9 7 9 9 0 0 6 4 2 5
3 5 1 9 7 8 4 9 1 9 8 7 9 6 9 5 6
4 7 4 4 8 6 5 1 4 9 8 8 7 3 4 5
7 7 5 1 3 3 7 9 6 5 3 4 0 2 4
9 8 0 4 2 6 1 5 6 1 0 5 0 4
8 7 0 8 1 7 2 8 0 1 1 9 1
0 3 2 3 2 2 8 1 8 7 5 6
2 6 4 7 4 3 7 0 5 4 3
7 3 8 0 5 6 8 2 6 8
1 2 6 6 2 4 3 0 2
0 5 1 0 5 8 0 1
3 8 2 8 4 5 7
2 3 8 9 1 6
2 2 1 3 8
5 6 6 8
9 3 5
7 6
9
5 7
7 0 0
2 5 9 3
0 3 7 6 1
5 2 5 9 5 3
5 5 3 6 6 8 5
2 1 0 2 6 8 9 6
2 5 8 8 6 6 1 6 7
1 2 5 2 4 9 2 7 0 0
4 9 0 8 1 0 0 1 7 3 5
6 9 5 0 6 6 2 3 6 7 5 2
5 6 6 6 7 8 6 4 5 5 8 0 0
4 4 2 2 8 6 5 0 9 9 9 3 8 7
1 5 1 9 9 8 5 2 3 1 0 7 3 8 8
5 9 6 9 3 1 1 9 1 2 4 6 8 0 8 9
5 0 4 6 8 6 7 3 3 1 7 3 1 3 4 2 7
7 3 3 6 5 5 3 6 0 9 5 6 3 3 2 9 9 6
3 5 5 1 4 7 1 7 9 9 6 5 2 2 3 7 0 9 7
6 9 5 6 9 9 3 5 8 1 8 9 6 1 8 4 5 3 4 6

16 271
5 2 1 7 5 4 8 3 8 5 2 3 1 3 2 0
0 0 8 5 2 8 8 7 1 0 8 6 3 2 2
2 7 0 8 4 7 4 3 4 4 4 6 0 5
5 3 7 2 1 9 0 8 8 8 0 9 1
6 7 8 6 5 9 8 0 5 4 6 7
6 4 0 1 8 8 4 9 4 6 4
0 9 2 9 1 2 4 3 9 9
7 7 6 6 7 9 3 9 4
5 4 6 9 8 6 8 2
6 7 5 8 6 8 2
4 3 5 6 6 2
6 4 9 2 4
2 9 6 6
2 2 5
6 5
2
9 5
7 4 4
3 4 9 2
1 3 3 7 3
3 0 5 4 5 1
2 8 5 6 0 1 8
9 2 7 3 8 4 2 6
7 6 3 0 2 9 3 9 9
2 2 2 9 4 9 4 8 4 6
3 4 2 8 3 3 7 8 3 7 5
9 1 4 9 1 7 6 2 5 2 2 8
6 1 5 5 9 6 2 6 8 9 0 6 4
0 6 6 3 5 4 1 8 8 4 4 7 3 2
4 3 2 5 1 2 4 9 5 0 6 8 5 4 1
9 1 9 2 3 2 2 2 9 1 7 5 0 9 9 8

6 60
0 1 8 0 6 8
4 5 5 0 8
6 0 5 4
6 2 9
3 2
5
6 3
5 7 2
8 5 4 8
9 2 8 6 8
8 8 5 9 9 4

4 37
9 8 7 8
3 1 3
0 6
6
3 4
0 8 3
7 6 6 0

7 70
0 7 3 6 8 7 9
4 8 0 8 5 7
2 4 2 9 2
0 1 5 0
1 4 0
0 5
7
4 7
7 5 2
8 3 5 9
7 8 9 6 0
9 0 1 9 1 6
0 1 4 3 4 7 9

14 181
0 7 5 5 4 9 4 2 0 9 7 3 3 7
7 0 5 3 1 2 6 4 2 4 6 0 3
5 2 7 1 1 4 9 6 5 9 8 7
8 4 0 2 9 0 5 8 2 6 2
9 6 9 8 3 9 5 7 0 1
2 0 7 6 5 6 3 2 8
5 5 8 8 0 1 9 4
5 6 7 7 1 8 3
6 3 3 8 3 5
9 6 1 1 9
4 3 9 1
9 2 6
0 7
0
9 3
8 7 3
0 8 6 8
3 0 6 8 5
3 9 8 6 0 5
6 3 8 9 6 0 5
9 9 1 7 5 4 8 8
4 1 1 7 0 2 5 6 8
8 0 5 3 4 3 7 5 6 0
6 1 0 9 8 7 9 5 3 7 1
1 7 3 1 6 9 1 4 2 7 0 8
6 4 9 7 0 1 3 1 1 9 9 9 5
9 3 5 6 1 4 3 9 5 4 5 5 0 3

10 132
2 4 3 0 5 8 0 3 0 6
5 4 0 8 8 4 8 1 7
7 8 0 9 0 0 0 2
0 4 5 4 2 1 6
8 4 6 6 6 2
8 8 5 2 7
6 9 2 1
6 0 7
6 0
0
5 5
8 4 4
3 9 6 3
6 8 4 1 1
5 5 4 2 9 2
4 0 5 7 6 0 4
4 7 5 5 9 1 8 4
4 6 5 1 0 4 9 9 5
8 7 5 4 8 6 0 2 6 2

7 112
1 5 9 5 9 8 9
7 4 0 8 4 7
2 0 8 8 6
0 2 3 9
1 3 7
9 3
3
1 2
5 6 2
0 6 1 7
7 0 5 6 1
2 2 6 1 0 5
5 3 3 1 2 5 7

11 139
7 1 2 2 8 0 9 4 9 3 1
4 1 4 3 0 4 8 7 3 2
8 2 3 9 8 5 0 8 3
5 1 5 8 3 7 1 6
0 9 0 5 3 1 4
2 0 1 5 9 0
4 2 6 0 5
2 4 2 3
8 5 0
5 3
2
9 7
3 7 4
9 8 8 8
0 9 7 3 0
7 6 1 2 4 2
8 6 3 9 8 3 5
1 0 9 6 2 5 4 8
5 3 1 7 0 8 0 4 6
9 6 8 5 2 2 2 1 7 8
5 9 9 2 9 6 9 5 0 6 2

16 270
3 1 6 1 0 2 2 1 0 3 5 5 0 0 8 0
1 6 4 4 9 0 9 2 5 1 4 0 2 1 5
1 6 3 0 8 2 5 6 4 2 4 5 2 1
1 5 0 5 1 7 2 3 7 3 0 9 8
4 4 9 5 0 5 1 2 4 0 6 0
1 9 9 3 7 0 5 6 0 8 5
7 9 1 0 2 6 9 0 9 5
9 9 1 1 4 7 5 1 3
9 8 4 3 4 4 0 1
7 4 1 7 5 0 9
5 8 1 2 7 0
9 6 7 8 8
4 8 5 1
3 5 1
4 7
2
4 6
4 8 1
4 8 6 6
6 0 9 7 9
9 3 4 1 4 0
7 6 2 2 8 6 2
3 8 9 3 7 3 7 6
4 1 3 0 3 2 0 2 3
4 3 7 5 2 0 7 6 0 8
6 8 9 4 3 9 3 3 0 0 7
0 7 2 3 7 3 1 5 9 1 8 1
8 3 8 8 8 4 7 2 1 2 6 7 0
8 3 4 1 9 2 2 1 1 3 5 1 1 0
8 1 2 4 4 5 0 5 5 3 0 8 9 0 7
2 8 0 5 9 8 9 1 1 5 3 7 9 0 7 4

11 149
2 1 4 6 2 7 1 1 2 5 8
5 8 4 6 8 5 8 5 9 7
2 1 9 7 2 3 5 2 7
9 6 5 2 8 3 5 7
3 5 9 7 9 1 0
3 8 2 8 6 1
5 6 9 1 8
9 2 9 8
8 4 2
8 6
1
7 3
1 4 9
7 5 9 8
1 5 5 2 2
6 7 3 7 9 4
7 2 4 9 3 7 4
2 1 9 6 7 9 9 4
6 2 7 7 3 1 2 9 7
1 2 6 6 3 7 4 2 2 5
6 4 1 5 3 2 3 2 9 2 9

18 215
5 9 4 2 9 0 2 5 3 1 9 0 4 7 5 9 0 8
8 2 8 5 4 4 1 4 7 5 9 1 4 9 0 6 0
7 3 1 1 8 6 0 3 1 6 8 4 1 5 2 6
0 4 3 0 6 9 5 6 3 5 2 8 5 0 6
5 6 4 2 2 5 5 6 1 3 6 0 3 0
1 4 3 7 0 9 2 5 2 2 8 4 2
8 5 8 2 7 2 2 0 3 9 1 0
1 5 4 4 5 9 9 2 6 9 0
3 5 6 8 8 9 5 6 9 1
4 2 0 7 8 7 8 1 8
3 3 5 1 7 2 5 1
5 8 2 4 0 8 1
5 3 3 5 8 5
7 9 9 2 4
4 1 6 9
2 6 8
5 2
0
1 2
8 2 9
7 6 8 8
7 8 5 4 5
9 1 0 0 6 1
8 7 1 7 1 0 7
7 9 3 6 0 3 4 4
9 6 5 9 8 0 3 8 6
4 3 1 4 3 1 2 0 7 4
8 4 9 3 9 7 1 5 7 3 2
8 5 9 7 9 3 7 5 0 1 9 8
4 6 2 1 3 9 0 7 2 8 0 9 2
0 9 4 2 0 6 6 4 6 1 3 6 4 5
8 9 7 4 4 1 6 7 5 4 0 2 3 3 2
2 3 9 8 9 3 9 7 5 5 2 9 5 8 9 7
0 4 1 0 3 8 2 7 3 2 3 5 6 0 7 2 9
6 6 4 2 7 5 9 6 0 7 6 1 5 0 2 5 7 8

3 39
9 2 5
2 9
3
0 2
2 6 0

2 28
5 1
6
5 4

11 164
9 2 1 9 7 1 6 4 3 1 7
5 5 5 2 9 0 8 3 9 9
2 4 4 2 5 5 3 6 2
8 4 1 2 6 6 9 1
4 3 4 6 8 4 3
8 4 7 4 6 4
6 6 3 8 0
6 1 1 6
9 0 5
8 1
1
1 5
8 3 4
9 0 8 1
9 3 8 7 4
7 0 7 6 3 9
2 6 9 8 9 5 1
7 0 0 7 1 2 6 9
4 3 0 2 2 2 3 3 3
1 0 2 3 0 9 9 2 6 5
6 6 3 4 8 8 8 8 3 5 1

15 167
3 7 4 0 6 1 9 4 6 2 4 3 0 1 3
5 8 3 7 4 7 1 2 3 9 0 8 2 8
6 0 7 8 1 6 5 1 4 0 5 7 9
0 5 3 9 4 8 4 3 8 8 0 7
4 3 3 2 0 8 6 4 6 9 7
7 7 9 2 5 5 6 7 6 4
5 0 6 2 5 3 6 6 8
6 3 4 9 1 5 4 4
4 3 9 6 7 4 7
6 3 4 2 1 9
5 9 6 1 1
8 3 6 0
6 9 0
9 4
6
9 3
6 1 3
6 3 0 7
5 2 7 9 5
3 3 1 6 9 5
8 3 8 7 1 1 4
3 5 7 0 1 7 8 6
5 1 6 9 9 1 1 2 9
5 3 0 4 6 3 2 8 9 5
0 0 8 1 8 5 7 0 4 7 4
3 4 2 5 4 0 2 4 9 4 6 3
8 8 9 1 9 3 2 0 6 0 8 8 0
3 1 2 4 9 5 5 2 9 8 2 9 0 0
6 7 4 2 6 3 4 3 6 1 1 4 1 2 9

15 241
0 9 8 9 5 2 0 7 4 0 9 2 5 3 5
8 2 4 6 8 3 1 7 8 7 2 5 0 8
5 3 0 6 1 9 5 1 7 4 0 3 9
0 8 3 0 8 1 4 3 4 2 6 4
6 5 4 8 2 0 9 8 2 1 4
0 6 2 4 2 0 6 6 6 2
7 1 1 9 7 2 5 1 3
0 8 9 8 4 1 6 6
7 1 0 2 8 3 3
1 2 6 3 1 5
4 5 3 4 4
7 3 4 3
2 1 4
0 7
8
9 7
0 3 1
3 6 1 0
8 3 3 1 3
2 1 4 9 6 2
4 9 2 2 1 9 0
0 9 5 2 5 1 7 1
3 1 6 5 3 0 3 4 2
4 3 6 2 5 9 3 7 6 3
9 1 0 5 8 1 9 0 5 4 8
8 4 8 3 8 7 5 0 2 5 0 1
5 2 4 6 2 4 5 5 4 9 4 9 2
9 6 9 1 3 0 6 2 3 3 9 0 5 7
0 9 9 0 1 7 9 3 4 1 5 5 3 4 9

10 145
4 8 1 3 6 3 7 1 5 1
1 0 2 5 0 1 0 7 3
4 3 1 1 8 7 9 0
5 9 2 1 2 0 3
4 7 0 0 1 8
3 1 1 8 8
3 3 5 9
2 8 3
4 5
9
0 6
2 4 5
9 8 5 1
8 7 6 7 5
9 4 3 1 0 5
4 6 0 8 1 1 7
4 4 5 4 2 9 0 7
9 4 7 0 5 6 4 9 2
5 5 1 2 1 4 3 3 2 1

14 208
9 3 5 5 0 6 1 7 3 1 6 2 0 4
6 8 2 9 6 8 1 9 6 3 9 8 7
5 3 0 0 5 4 1 3 5 7 3 7
8 4 2 8 0 4 1 6 5 8 3
7 2 1 9 7 1 2 1 1 2
1 3 5 6 0 1 5 3 0
8 5 3 2 2 6 7 9
2 9 6 1 2 1 0
0 8 0 0 5 9
8 1 2 4 3
0 2 0 0
4 1 9
6 5
3
9 7
4 8 9
4 0 8 7
7 5 6 0 3
8 0 9 4 9 3
5 4 7 8 6 1 4
7 3 9 7 0 5 4 4
6 5 8 4 7 8 7 5 2
1 7 7 6 9 4 9 3 1 1
4 9 5 5 0 2 3 9 6 9 8
8 1 3 6 0 0 9 5 4 8 7 4
9 9 8 3 8 5 2 1 5 3 1 6 7
3 0 5 2 2 1 5 0 2 6 2 8 3 6

12 172
5 3 7 7 8 8 4 0 3 5 8 9
3 1 7 0 9 3 3 5 7 3 6
4 9 4 0 0 9 7 8 6 5
2 2 3 5 3 7 9 1 0
5 0 9 3 6 5 5 9
6 1 9 9 1 7 5
9 4 7 5 0 3
2 0 3 8 8
5 9 4 0
3 7 7
9 5
9
0 6
8 7 6
9 0 9 1
7 9 8 5 9
0 4 0 5 2 5
8 0 7 4 9 3 4
0 1 1 4 7 1 0 6
4 3 8 0 1 0 4 5 3
5 9 4 2 7 0 8 2 3 0
1 2 5 7 5 1 8 5 3 1 6
0 8 4 8 7 5 7 5 5 0 2 4

15 175
4 9 5 4 1 2 4 7 9 0 2 2 4 7 7
0 1 7 1 7 8 5 1 5 7 4 3 7 2
9 2 2 5 2 5 0 4 0 8 8 4 4
3 3 5 2 2 0 5 0 4 3 2 6
8 8 1 5 6 2 3 8 9 1 1
5 6 8 1 8 7 1 9 9 2
0 4 1 2 8 0 0 4 6
0 0 3 9 8 5 4 5
4 4 8 0 9 8 9
7 0 9 8 4 9
2 0 8 0 7
3 0 2 5
0 7 0
2 7
9
0 0
6 4 1
5 1 2 9
7 0 6 3 6
3 6 7 6 6 3
3 2 4 8 1 7 1
9 0 6 7 1 3 3 8
1 7 9 1 3 0 1 8 3
0 3 4 6 7 3 2 5 4 8
2 7 9 3 6 5 4 6 4 1 9
8 7 6 0 1 3 5 5 6 8 6 8
2 4 6 5 3 3 9 4 8 9 2 0 1
5 5 9 4 7 5 0 9 0 1 4 1 3 2
9 8 6 3 9 9 5 1 1 0 7 6 9 2 2

2 28
9 3
2
3 4

15 203
0 1 6 8 9 5 7 6 3 8 2 1 4 5 4
0 9 1 1 8 5 5 5 4 3 0 9 7 7
9 1 1 9 8 4 7 9 2 5 9 9 4
7 6 8 7 4 9 6 2 3 6 7 1
8 8 1 3 4 8 4 8 8 5 4
4 1 0 1 2 1 0 2 0 5
0 1 0 8 7 0 5 2 5
4 2 4 2 9 8 5 6
6 1 0 4 1 6 6
5 3 1 4 6 2
9 1 6 7 7
7 7 0 5
7 7 0
3 3
7
3 1
5 1 7
8 0 4 1
9 3 0 8 0
8 2 1 0 6 3
8 5 4 9 4 1 5
8 0 8 5 8 1 1 5
1 6 2 9 1 7 0 5 4
2 7 6 8 2 7 9 5 8 1
8 3 7 9 3 5 8 3 0 9 5
6 9 3 8 9 8 1 7 3 6 8 6
3 2 6 0 8 7 0 4 8 1 8 1 3
8 7 8 9 5 1 9 6 6 9 5 5 2 8
1 6 2 7 8 8 0 5 0 9 9 7 3 3 6

4 55
8 3 9 2
6 6 5
9 1
4
9 8
7 4 4
2 7 2 7

17 277
9 8 1 6 2 2 7 4 8 3 9 8 4 6 8 6 8
7 5 8 7 5 7 1 7 3 7 0 9 6 9 2 2
0 1 6 1 5 5 9 6 4 6 7 2 6 8 6
9 2 8 8 4 4 0 7 9 9 8 4 1 1
5 6 7 3 2 0 8 8 9 3 1 3 6
1 0 1 5 2 2 2 0 4 2 7 1
8 3 3 4 9 6 3 3 2 2 6
5 2 2 4 5 6 2 3 8 5
7 8 1 1 0 0 0 3 7
9 6 7 8 8 7 1 5
2 3 1 6 6 4 2
1 9 7 2 8 2
8 2 6 0 7
9 4 1 8
6 1 0
7 8
9
5 1
8 4 1
6 4 7 5
7 9 3 0 4
4 9 5 0 7 4
9 6 4 7 5 5 8
5 0 2 1 7 0 2 1
8 1 2 6 6 0 8 1 1
8 2 8 0 8 8 5 2 8 0
3 7 3 5 4 3 2 5 4 5 1
8 8 4 0 1 8 2 9 7 6 2 2
4 1 7 4 2 1 4 2 9 4 7 0 3
1 6 1 7 7 2 5 3 7 7 9 1 3 8
2 4 7 2 2 2 7 4 1 8 8 1 7 3 2
1 0 9 1 5 7 8 9 1 7 3 7 8 7 4 6
5 2 1 9 9 9 7 2 6 0 2 5 1 0 0 1 0

11 156
4 1 5 0 9 5 2 4 3 0 0
1 6 8 7 1 7 0 2 7 7
6 4 5 9 6 0 5 5 8
5 4 3 3 6 3 7 6
2 7 9 6 7 5 0
8 5 0 7 3 6
6 2 5 1 7
0 3 7 2
5 4 5
4 6
0
6 7
5 7 8
8 1 6 9
2 2 3 8 2
1 1 6 4 7 8
6 8 2 3 7 1 1
9 7 0 7 9 0 4 0
7 7 9 6 9 8 1 8 2
1 7 3 3 6 9 3 1 6 4
8 8 5 1 1 0 3 6 9 6 9

17 259
9 5 4 8 4 2 6 8 6 3 3 1 6 0 6 9 2
0 3 3 6 6 6 4 8 6 0 0 6 9 8 7 8
4 9 7 8 0 1 1 0 3 4 9 7 0 3 2
7 0 5 2 2 9 0 1 5 5 6 7 3 9
6 8 5 9 6 6 0 3 6 2 1 3 8
7 5 9 9 7 5 2 2 7 0 3 5
5 2 6 5 2 7 0 9 5 5 7
7 7 3 6 5 5 6 1 3 5
3 0 6 1 7 3 8 4 3
4 6 4 8 5 2 5 1
6 3 0 4 4 7 2
4 6 1 6 6 6
3 3 1 6 5
5 6 8 8
9 1 4
7 0
4
5 5
5 4 7
5 2 9 8
0 2 6 5 2
5 8 9 9 8 6
3 0 0 1 3 8 6
8 8 2 5 9 7 1 4
2 0 9 8 1 7 6 5 6
5 3 3 5 6 3 5 5 7 0
1 0 3 7 3 1 3 4 9 6 0
2 1 9 8 8 8 7 5 0 9 0 3
7 2 5 2 3 5 7 7 9 0 1 1 4
4 5 9 5 6 4 7 6 8 0 0 0 8 6
7 8 3 3 8 2 6 3 8 5 6 7 0 6 1
1 3 9 5 0 1 3 8 8 6 7 9 7 0 6 0
1 4 6 4 2 8 2 2 6 8 7 9 2 9 3 8 6

7 107
6 8 8 6 7 3 3
1 1 5 0 4 0
3 4 4 4 2
4 9 1 3
7 1 2
3 8
1
4 1
5 0 2
6 6 0 7
3 7 2 0 0
8 5 9 9 1 9
5 6 9 3 9 3 4

5 55
6 5 2 6 7
2 4 8 8
2 8 0
7 7
1
6 6
6 7 4
0 7 5 1
3 3 9 6 2

18 312
7 0 6 3 7 3 0 0 5 9 1 1 2 2 2 0 5 1
8 8 1 2 7 5 5 0 1 2 0 8 7 2 0 9 7
3 0 6 2 3 9 2 9 3 3 3 4 6 6 5 4
0 2 2 5 3 9 5 7 8 9 4 6 3 4 2
0 5 6 9 8 5 2 8 9 9 2 3 7 0
6 3 0 1 6 7 5 6 3 9 0 6 3
6 5 7 1 1 1 0 6 3 8 8 7
4 8 9 0 9 5 6 5 2 4 8
7 0 8 3 8 7 1 8 2 7
5 6 0 2 4 2 7 6 3
6 8 6 4 5 3 0 8
6 9 8 8 2 1 6
3 2 6 0 6 2
8 8 6 2 6
1 3 4 8
7 2 5
1 5
7
1 7
4 8 0
4 6 4 1
5 6 4 5 6
5 0 4 9 2 1
7 7 7 7 6 3 5
2 1 7 9 6 1 5 6
9 6 1 8 0 4 7 5 7
3 5 7 4 0 5 8 4 3 1
6 3 8 0 1 0 3 3 9 2 3
7 8 9 3 7 0 3 7 1 3 3 0
4 9 8 3 8 7 0 8 4 2 8 6 4
8 6 7 5 7 7 1 5 0 0 5 8 9 8
2 8 7 6 3 5 8 0 1 0 7 2 9 3 8
6 0 7 3 6 0 8 6 6 0 9 9 3 2 8 0
7 5 5 2 6 0 9 5 0 7 4 5 5 6 0 8 9
0 3 7 7 3 5 3 4 6 4 2 5 1 5 1 5 4 8

6 83
0 5 6 5 0 9
7 5 7 9 3
4 8 3 8
6 0 7
9 6
5
5 7
3 6 0
3 3 9 9
3 0 1 1 8
3 8 8 2 0 8

3 52
0 8 5
1 5
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7 123
9 7 8 1 5 2 3
0 7 5 4 4 5
3 2 0 7 7
5 2 6 6
0 1 4
1 1
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6 5
6 9 4
6 2 2 2
1 0 5 0 8
9 7 7 8 2 1
4 3 8 0 7 8 7

16 287
0 0 6 0 8 1 0 6 0 4 8 7 3 5 9 7
8 6 4 8 6 5 3 3 1 8 6 3 9 7 3
1 7 5 2 5 0 2 1 5 0 3 8 7 5
3 2 4 9 0 8 5 3 3 7 5 0 5
0 2 8 1 3 6 3 1 8 6 0 9
7 7 2 8 9 2 3 8 9 8 6
0 2 5 7 7 4 4 2 2 6
4 5 4 8 3 4 1 5 0
7 8 8 7 4 2 7 8
1 9 8 0 2 0 2
4 7 5 7 0 7
0 0 5 4 3
4 4 0 8
2 5 0
3 8
1
4 7
3 0 4
7 7 0 9
5 7 7 5 0
8 9 3 8 4 9
0 6 5 0 8 3 0
2 2 6 7 1 4 1 0
5 2 3 3 4 7 8 4 2
6 8 7 1 7 3 2 2 0 1
5 5 6 7 1 3 8 2 7 3 6
3 4 7 5 6 9 2 8 2 4 1 6
8 5 4 4 4 8 1 1 0 3 5 8 9
9 0 9 2 8 3 0 1 4 5 4 1 5 4
6 8 7 4 9 3 5 6 2 8 3 6 6 6 5
5 7 3 1 9 8 9 7 2 2 6 2 1 5 9 4

5 73
9 9 5 2 2
2 7 1 8
4 1 0
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7 8
4 5 5
9 7 5 6
3 1 9 4 4

15 211
1 2 9 8 1 0 4 5 3 2 8 2 0 1 7
2 7 9 1 8 0 5 5 0 0 1 8 5 8
1 4 7 5 1 2 0 1 7 5 9 1 3
5 9 3 2 1 5 9 7 4 5 4 2
7 4 5 5 5 9 8 5 5 1 6
9 9 7 2 8 9 3 1 1 1
6 8 9 8 6 1 1 3 1
1 9 6 7 2 1 5 5
8 9 1 0 4 4 8
3 6 3 3 1 1
2 3 9 3 0
6 0 6 2
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1 2
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5 5 0 6 8 6
8 4 3 6 6 5 5
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9 2 3 8 9 3 6 8 1
0 4 1 7 7 9 1 2 9 5
3 9 0 1 8 5 7 5 7 0 8
6 5 2 2 5 8 5 6 0 1 3 6
8 7 3 4 6 6 5 7 8 6 8 4 4
3 9 5 2 3 7 7 6 7 0 7 9 6 8
0 2 4 5 8 4 8 9 7 2 1 0 9 6 3

12 178
1 8 4 8 2 3 6 7 7 5 3 2
6 5 1 6 4 4 2 3 0 0 6
9 4 8 0 2 6 5 3 3 4
1 8 1 5 3 3 3 6 3
5 3 2 7 4 9 7 6
4 4 1 5 2 0 0
7 5 5 3 1 2
5 9 8 8 6
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4 4
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7 2 9 7
8 3 8 9 9
6 5 4 6 7 7
2 1 0 1 5 5 3
7 6 8 7 3 8 4 7
9 4 0 1 3 5 7 0 1
7 7 0 4 1 9 1 0 0 6
3 8 3 0 2 5 1 5 6 8 4
1 3 3 8 6 7 8 2 8 2 4 4

14 159
8 7 0 1 6 2 6 4 4 5 2 9 8 4
1 6 5 8 9 0 3 8 5 5 2 4 2
4 5 0 3 4 2 4 1 8 0 4 1
1 2 3 6 0 1 5 9 8 4 7
3 9 6 8 5 4 4 7 9 8
1 2 2 2 7 2 7 8 2
8 3 3 8 1 0 6 9
9 9 7 4 6 1 9
5 8 9 9 1 9
7 9 3 4 5
0 3 9 4
2 8 4
7 2
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6 2
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9 1 3 7
3 5 4 8 5
4 1 4 2 3 4
6 3 1 1 3 5 6
6 8 1 1 0 0 3 7
1 1 2 9 6 9 4 3 0
1 7 9 7 5 1 5 8 2 0
4 5 9 0 5 1 1 0 7 9 7
5 6 2 2 9 6 4 4 4 0 9 3
6 3 1 2 5 7 7 8 8 6 0 7 9
4 9 9 4 9 2 9 8 7 3 2 8 3 7

8 118
4 4 7 3 4 6 3 1
2 2 4 0 9 5 5
3 1 2 1 7 0
8 4 3 7 6
1 9 3 6
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3
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6 6 7
6 6 0 6
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8 6 9 6 2 9
6 2 0 6 9 4 3
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18 175
8 3 1 3 2 5 2 0 1 6 1 7 3 9 5 1 7 3
3 6 6 6 5 3 4 7 4 7 2 6 1 9 8 1 1
7 6 8 2 5 0 1 7 0 6 7 4 6 5 9 5
1 4 2 7 0 6 8 1 8 4 9 5 1 8 1
0 2 4 1 5 6 3 6 8 9 3 0 5 0
1 0 5 7 8 6 6 9 3 8 3 1 0
5 0 0 6 0 5 0 5 0 3 6 0
8 6 7 6 1 9 4 4 6 3 6
3 4 5 7 0 7 9 3 8 0
4 2 6 0 0 1 9 8 0
8 2 1 2 1 6 4 9
3 0 5 7 9 8 9
2 6 8 8 9 0
3 2 9 3 4
5 3 0 9
9 8 7
4 6
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6 6
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2 5 6 9
1 2 1 7 9
9 3 1 7 7 4
8 4 2 5 7 6 9
3 2 2 1 2 7 8 4
8 5 9 1 8 1 7 5 9
8 3 6 7 7 8 5 5 0 0
0 7 6 4 2 6 6 9 0 3 3
9 8 5 9 1 0 7 0 1 2 3 4
7 1 6 3 6 8 8 2 4 5 2 3 0
2 2 8 6 3 1 0 4 4 5 1 2 2 8
9 1 9 9 8 4 4 7 8 6 8 8 3 9 4
0 9 5 5 7 8 0 8 8 7 3 5 9 0 9 0
3 7 2 6 7 9 9 1 2 3 2 9 7 9 0 5 3
4 3 3 5 1 7 1 5 5 7 6 4 5 4 6 2 0 5

9 116
6 6 4 1 7 7 7 9 2
6 4 3 2 8 3 1 6
1 1 1 1 3 5 6
9 3 0 0 3 8
1 1 3 2 0
8 3 8 9
3 0 7
5 4
1
0 7
1 8 7
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9 9 3 6 4
6 9 3 3 1 3
4 5 8 2 0 5 4
2 5 0 9 0 9 7 1
4 2 1 0 3 5 6 9 6

7 81
8 3 1 0 7 6 0
2 3 6 3 5 8
2 1 1 0 3
1 9 4 7
2 9 7
3 6
0
2 9
3 0 8
6 7 6 2
6 1 0 7 6
5 1 7 2 4 3
3 3 2 9 2 0 6

7 77
7 9 5 5 0 2 7
8 1 2 7 7 0
7 1 7 3 1
7 3 8 2
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2 7
7
5 3
6 8 4
1 1 7 2
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5 1 1 3 1 0
2 4 8 4 3 4 9

11 154
5 7 8 5 7 1 8 4 7 6 0
6 2 5 5 1 2 8 4 4 4
3 8 8 5 9 1 3 7 9
9 7 5 6 0 8 7 1
5 0 9 9 6 3 2
0 4 8 9 8 3
0 4 4 7 0
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8 8
6 5 3
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7 0 4 3 1 6
7 1 8 2 4 1 5
4 0 0 4 8 9 6 2
7 4 8 8 0 4 2 4 7
0 4 5 4 3 9 6 8 4 3
0 5 0 8 8 3 4 5 8 4 0

19 194
9 5 0 1 4 0 8 8 2 0 9 3 2 5 1 4 0 0 9
2 1 4 5 2 3 4 1 9 5 6 5 4 7 9 0 8 0
1 0 4 6 7 8 6 6 8 9 0 6 7 4 4 8 8
3 0 1 3 6 8 9 8 6 0 7 2 3 2 2 6
9 1 1 5 4 5 2 4 8 3 4 9 9 7 8
4 7 5 2 8 1 7 0 1 1 8 9 0 9
0 1 3 6 2 6 1 0 6 6 5 5 3
6 2 9 4 9 1 8 7 8 7 1 0
2 9 0 1 1 4 3 0 2 3 8
4 5 3 9 4 2 4 7 0 2
4 9 8 3 3 7 7 0 6
3 8 8 0 2 7 5 6
9 0 7 5 0 7 2
7 3 0 5 2 9
7 4 8 4 3
1 3 4 4
8 0 0
8 6
4
1 8
5 8 0
7 5 8 5
5 5 0 9 4
1 5 5 7 1 1
0 7 1 5 4 8 8
1 1 6 5 2 7 1 3
8 4 9 2 6 4 9 6 1
7 2 5 3 6 1 3 9 2 8
2 9 0 7 8 5 7 9 2 5 9
1 8 1 1 6 2 6 4 0 1 8 9
3 9 2 8 7 1 2 0 6 7 2 5 2
0 9 4 4 9 3 8 8 4 6 7 0 9 2
8 7 4 9 6 6 0 1 9 3 6 3 1 1 2
6 8 8 9 5 9 5 4 8 4 5 5 9 1 4 5
4 0 5 1 4 1 6 5 9 0 3 6 4 7 9 9 7
2 3 7 8 6 7 1 2 9 7 7 0 7 9 6 3 1 8
5 1 4 8 2 8 2 5 1 9 3 8 5 4 2 6 5 8 2

19 304
8 4 4 8 5 3 5 4 3 4 8 0 9 1 2 8 6 0 3
3 7 2 6 1 9 9 0 0 7 1 5 4 6 1 7 5 3
9 0 1 8 6 4 4 7 5 0 1 3 5 4 0 8 6
7 5 2 0 4 2 2 4 6 1 2 9 7 9 2 0
8 4 6 0 3 5 7 2 7 7 9 3 3 1 2
6 1 8 2 3 2 3 5 8 5 7 5 7 4
4 2 3 4 3 4 9 9 3 7 1 8 9
5 6 5 6 2 2 8 8 1 9 8 3
6 9 0 1 0 0 7 1 1 1 8
9 3 8 9 0 8 1 7 5 0
4 6 7 4 5 5 1 8 5
5 4 4 0 5 9 1 9
8 6 1 1 8 3 9
7 8 6 4 5 5
9 0 6 9 8
3 9 1 9
7 4 4
5 2
7
3 2
2 6 2
5 9 1 1
1 4 3 0 2
3 0 9 7 1 8
0 3 5 7 2 2 8
1 8 8 3 3 1 7 6
8 8 8 6 7 3 7 3 2
5 6 8 5 9 3 8 0 4 0
4 0 7 2 4 4 7 8 5 4 2
6 1 7 6 3 3 8 3 2 0 8 4
1 9 5 4 6 5 6 2 3 5 7 7 5
5 4 0 3 0 3 6 4 7 8 9 4 2 4
4 6 1 0 4 5 2 0 9 6 0 0 4 8 6
1 2 6 6 3 9 0 4 1 2 5 4 1 5 2 3
4 2 0 1 7 8 1 4 1 0 0 8 7 9 1 0 6
5 1 1 8 5 5 7 8 5 6 3 9 5 1 5 7 4 6
6 1 1 7 2 2 1 2 5 1 1 7 7 5 0 1 0 7 1

2 26
1 7
5
3 1

3 47
6 8 1
1 0
8
9 2
8 9 3

15 178
1 7 0 3 0 6 7 6 9 3 4 5 0 5 2
6 6 1 0 0 8 8 9 0 3 4 6 4 3
1 3 9 4 4 8 3 1 0 7 7 5 2
1 6 8 5 5 4 3 8 7 6 7 1
2 4 0 1 0 8 7 4 2 4 4
4 3 9 7 6 9 5 6 0 2
9 7 6 2 1 0 3 1 4
4 8 4 8 8 3 2 8
7 3 4 2 5 4 1
5 9 3 6 3 3
4 2 1 6 0
5 4 0 0
0 8 7
2 0
7
0 2
3 3 7
2 0 5 1
9 6 1 4 4
5 7 0 7 9 4
2 6 8 1 4 5 2
1 3 0 8 2 7 9 1
6 4 9 0 3 4 9 6 4
9 5 6 5 8 5 4 4 6 9
2 8 1 4 2 4 2 7 9 7 6
9 4 1 4 3 9 5 7 7 0 5 0
6 6 6 1 9 8 5 5 1 3 4 8 0
6 5 5 3 2 4 8 8 2 4 6 7 2 1
0 0 8 2 1 0 7 2 5 8 8 5 2 7 3

10 114
0 9 6 1 4 9 8 8 7 7
2 5 5 3 5 2 4 2 3
0 0 5 4 3 6 1 7
6 2 2 8 4 1 9
3 0 8 3 1 4
3 4 9 4 8
4 4 1 3
4 9 4
5 0
4
2 2
1 8 1
9 8 2 9
9 3 9 8 7
1 9 1 4 2 3
0 5 9 3 7 0 0
2 1 6 2 2 1 3 1
5 8 6 3 2 6 4 3 2
4 1 0 4 1 7 3 9 2 8

7 100
3 4 6 0 1 3 7
9 5 5 5 2 0
1 3 4 7 5
8 4 4 0
7 1 3
7 2
5
5 8
8 5 2
2 2 4 6
6 3 3 0 1
7 1 8 1 0 0
9 5 2 4 9 0 4

19 250
4 9 7 1 0 8 3 0 7 6 4 0 2 5 9 0 9 7 5
5 7 1 0 7 5 0 6 8 7 0 5 3 0 2 2 5 0
8 0 7 5 0 4 6 2 9 7 3 6 5 4 8 3 8
4 8 7 6 5 2 8 1 8 3 0 9 9 1 1 5
8 6 4 7 1 2 2 4 3 4 7 7 4 8 6
4 4 9 1 1 3 2 4 9 9 8 3 8 8
7 1 9 1 7 7 1 2 3 9 5 8 3
4 9 6 2 3 6 8 3 7 5 4 1
2 2 9 6 8 9 3 6 3 0 2
1 5 6 0 4 2 8 0 6 6
5 6 6 8 6 0 1 3 4
5 8 0 8 7 6 9 7
6 9 6 0 7 9 4
4 1 2 7 1 7
5 5 9 3 5
8 6 2 1
1 2 4
4 8
5
6 5
1 2 5
0 0 3 8
0 9 9 3 0
5 5 8 9 6 8
9 7 6 3 7 6 7
9 8 7 9 5 8 5 7
1 1 1 4 3 2 5 7 3
8 1 1 1 7 6 8 2 0 2
6 8 2 4 9 1 7 4 6 0 9
8 5 1 9 9 8 9 2 9 4 0 8
6 7 3 0 1 9 9 7 7 1 3 6 0
5 0 9 2 9 5 4 4 0 0 5 6 7 5
4 9 8 5 8 8 8 6 8 4 6 1 0 1 4
3 9 6 2 9 5 4 5 4 3 7 2 6 5 1 0
4 4 9 2 8 4 7 3 6 2 8 4 2 1 8 9 4
5 7 7 0 1 9 5 6 6 0 0 6 0 7 7 7 7 6
8 1 8 2 8 1 2 8 3 8 9 7 2 2 5 2 3 9 9

18 306
0 8 4 6 5 4 3 1 6 1 2 2 0 6 9 7 1 4
7 2 1 7 4 4 7 6 3 6 0 6 6 2 5 3 8
9 5 3 0 7 7 2 3 4 5 1 8 5 6 4 0
0 4 4 2 8 7 3 9 7 5 6 3 5 2 4
6 4 9 4 1 5 5 6 6 5 8 0 4 5
2 8 4 3 3 2 9 5 6 8 0 0 2
7 0 8 5 7 1 5 3 7 7 8 7
0 6 9 1 9 4 0 7 4 6 2
2 5 6 0 7 5 4 3 5 0
7 0 1 6 6 5 9 2 4
7 3 1 1 7 0 4 0
0 4 0 0 7 9 3
4 5 2 2 6 4
2 6 4 2 5
6 2 5 7
4 5 2
4 1
9
6 1
1 8 9
5 5 7 1
4 0 5 2 2
3 2 0 2 7 8
2 5 5 0 0 9 4
6 2 2 2 1 1 3 5
9 1 1 2 4 5 7 9 1
2 2 6 2 3 7 5 8 3 2
7 4 4 1 6 9 9 9 0 3 6
4 4 7 8 3 6 0 7 8 4 1 8
4 5 4 9 0 4 8 7 6 7 7 5 3
4 5 0 3 4 8 3 3 8 1 8 1 3 8
8 5 5 9 8 8 7 7 3 4 2 4 3 1 2
9 0 9 2 9 4 2 3 7 2 5 0 0 9 3 3
7 6 0 0 2 3 4 5 7 2 6 5 1 8 9 2 8
0 4 2 9 1 0 9 1 9 5 0 5 7 8 1 6 2 4

4 49
4 2 3 1
2 3 5
3 4
9
9 9
9 8 9
5 6 1 6

14 176
6 7 3 4 7 4 4 1 9 5 1 7 3 3
5 4 3 5 1 8 7 5 9 6 5 0 4
5 3 0 6 1 6 8 1 8 8 9 8
3 3 3 7 8 7 6 2 4 7 8
5 8 2 6 1 8 5 7 6 9
5 6 3 2 4 2 6 3 0
4 2 3 0 0 8 4 3
8 7 7 6 1 1 1
5 9 6 7 6 6
6 9 7 2 4
5 0 9 0
9 3 1
5 8
0
6 3
5 9 7
3 4 6 4
5 4 6 3 2
4 4 2 1 1 7
2 6 9 7 9 2 3
3 4 0 4 2 4 5 5
0 2 1 7 0 4 5 3 5
0 5 0 5 5 4 6 1 1 1
5 7 0 1 0 2 1 0 8 5 1
0 0 0 5 0 1 8 7 2 5 0 2
8 9 0 5 2 1 3 7 5 0 7 2 2
2 8 5 6 9 7 0 1 9 1 0 3 5 2

10 99
3 1 7 1 6 9 3 4 0 9
5 5 6 2 7 6 2 7 9
4 1 9 3 1 6 2 0
8 8 8 9 6 3 8
6 3 8 7 5 3
4 5 7 0 7
8 5 2 7
9 2 1
0 7
2
9 2
3 5 0
6 5 9 4
0 9 4 9 9
8 9 3 8 2 5
0 4 8 5 1 3 7
9 7 1 9 8 6 6 9
2 0 3 7 3 1 5 5 9
8 7 5 8 9 4 0 0 1 2

13 215
2 5 9 2 1 9 5 7 5 3 7 5 3
0 3 9 7 2 2 5 5 5 8 5 5
1 3 0 6 1 5 6 0 5 2 7
3 7 3 7 1 9 7 4 2 0
7 2 5 7 2 8 6 2 8
6 7 4 1 0 9 8 7
7 5 4 1 4 8 0
9 7 3 2 4 8
2 5 4 9 6
9 3 3 2
7 9 9
0 5
4
6 9
4 5 8
2 7 2 6
3 8 5 5 1
4 5 1 8 6 0
0 4 7 1 0 9 4
8 2 7 6 4 8 9 7
0 5 4 2 5 2 1 5 6
0 4 1 7 2 2 2 9 9 2
8 8 3 8 9 7 7 6 4 3 3
4 4 8 8 6 0 9 2 7 4 0 2
2 3 9 5 3 7 4 8 2 9 2 9 1

17 241
1 5 8 1 7 5 2 1 8 1 6 5 4 7 6 4 7
9 5 3 2 3 6 4 0 2 8 7 6 7 3 0 5
7 0 8 2 9 1 0 3 3 2 9 9 0 9 9
0 4 6 2 8 2 8 1 9 7 1 8 3 7
0 0 7 6 7 9 3 3 4 9 5 9 2
6 7 6 8 7 7 4 9 8 1 9 5
6 1 5 1 9 5 7 9 9 9 1
4 8 9 3 4 3 7 1 5 8
2 9 8 0 0 9 4 7 9
9 5 3 7 8 7 8 5
6 8 1 0 5 2 0
5 4 5 0 5 0
8 7 0 6 1
3 0 6 2
7 3 2
1 8
4
2 9
5 5 8
3 9 4 7
1 8 2 7 3
7 2 4 8 3 4
0 6 3 8 7 7 6
7 0 4 5 4 8 6 8
1 2 0 6 9 6 3 5 5
7 5 8 4 6 6 4 7 1 0
8 5 1 0 4 5 2 9 6 7 8
9 9 7 0 5 8 8 7 3 4 7 5
8 7 7 9 2 4 1 1 9 7 3 4 6
5 4 8 3 7 4 3 0 4 7 9 2 6 3
1 6 9 3 2 3 5 6 2 6 7 6 3 7 2
4 3 1 9 6 3 0 2 5 5 2 6 9 6 6 4
4 4 1 5 4 7 9 0 9 4 5 0 6 5 1 3 0

18 314
4 8 9 4 3 0 9 9 1 3 8 2 8 6 7 0 4 6
3 4 5 7 9 0 1 4 6 4 8 5 9 5 5 6 8
0 4 2 8 2 8 8 4 0 8 2 8 2 7 7 3
2 0 2 6 7 5 4 4 1 7 8 4 5 0 2
7 5 2 3 7 8 7 7 3 7 8 4 1 8
0 7 9 2 2 8 7 5 7 8 7 5 4
7 4 1 9 5 7 7 5 3 1 3 9
0 5 4 4 6 3 6 8 3 2 1
5 4 7 9 5 1 8 8 4 4
6 5 2 3 8 3 1 7 6
4 8 1 9 1 3 0 9
2 5 5 1 1 9 6
2 7 7 6 8 2
7 3 5 4 5
9 4 4 2
7 9 0
9 9
7
9 3
2 1 9
4 1 9 5
0 4 2 2 4
9 3 2 4 5 6
3 9 3 2 2 0 7
8 1 4 8 3 4 5 5
3 2 3 4 1 2 0 4 5
5 5 4 3 7 4 0 4 6 9
1 2 4 8 6 0 6 2 8 6 1
0 4 0 6 1 1 6 2 4 5 0 4
8 4 5 5 5 8 2 2 7 2 1 9 1
3 7 8 3 4 3 9 2 5 6 1 6 4 9
6 0 6 9 6 4 9 5 3 9 7 1 9 0 0
0 9 9 8 6 3 0 8 7 2 7 4 8 3 1 1
8 2 7 7 0 6 3 1 0 8 0 1 4 8 6 9 6
7 7 7 0 0 1 4 9 5 0 2 1 2 0 7 6 7 1

6 78
6 7 6 1 4 4
7 8 8 1 3
4 3 9 6
6 7 2
5 3
7
8 1
0 0 5
8 8 4 1
3 3 6 2 3
5 0 4 0 7 5

7 114
2 8 3 6 1 3 7
7 8 6 3 3 0
5 0 2 5 7
5 9 0 5
4 7 3
3 9
7
4 6
8 8 3
1 3 7 5
9 6 1 3 9
4 5 4 5 3 4
0 1 9 3 0 8 1

5 76
9 1 4 2 2
2 0 1 0
5 1 1
1 3
5
7 2
5 7 3
4 1 4 2
7 0 7 2 8

6 54
5 0 7 9 2 5
7 3 9 6 5
3 4 5 0
9 9 4
0 1
9
0 1
8 6 7
8 1 9 7
7 3 2 9 5
9 5 9 4 2 3

14 192
3 1 4 0 4 4 6 5 0 1 8 7 1 5
9 6 9 5 3 9 6 2 3 1 2 8 0
3 5 8 8 4 6 3 0 5 2 9 6
6 7 7 3 8 7 0 9 4 8 1
8 3 8 6 7 9 4 4 8 0
6 7 8 0 8 1 5 9 3
7 9 5 2 9 0 2 7
9 7 9 2 2 0 1
2 9 0 1 4 8
9 5 0 9 6
9 5 8 3
0 6 5
5 0
5
0 3
9 7 7
9 3 5 5
5 5 7 8 6
0 4 9 1 8 7
3 2 7 6 3 5 4
4 3 1 5 4 1 2 1
3 7 1 0 6 4 5 9 4
6 3 0 7 1 0 5 1 5 8
8 9 9 1 1 0 6 0 1 5 2
8 2 4 8 1 2 2 3 4 7 4 2
4 0 7 9 6 6 7 2 6 2 1 0 4
3 4 3 5 6 1 1 6 7 8 9 3 5 3

19 244
7 4 3 8 9 0 8 5 2 8 9 0 5 2 5 9 1 0 3
2 3 1 1 1 4 1 8 5 6 3 3 0 5 5 5 5 3
9 9 3 4 6 3 4 0 8 3 3 1 0 1 3 5 3
4 5 8 6 9 7 4 7 7 3 6 5 9 8 8 4
5 8 8 5 3 5 7 0 5 6 6 8 8 8 9
9 3 6 2 9 1 9 1 9 8 8 6 0 5
4 4 1 0 5 9 7 4 2 1 8 0 4
5 7 7 3 8 0 7 8 4 8 6 6
6 3 3 3 1 8 1 3 1 5 1
9 3 6 7 8 4 0 9 3 6
9 0 8 2 6 5 9 2 6
7 1 5 3 2 3 3 8
8 6 8 8 6 3 0
5 5 7 9 3 5
7 1 0 6 2
2 7 8 7
6 5 1
9 2
6
5 0
2 5 1
8 9 8 8
3 8 9 5 9
6 5 2 4 8 4
8 0 5 8 3 4 2
4 5 4 1 3 3 8 0
1 0 7 9 8 1 3 4 4
9 3 6 8 9 6 5 4 1 7
7 7 7 6 0 6 2 0 4 6 5
3 4 8 6 3 4 9 2 4 6 2 0
4 7 9 6 1 5 7 3 5 3 0 8 3
0 6 3 6 0 7 5 2 6 8 7 1 1 5
8 1 9 3 1 9 2 5 3 9 6 8 4 3 5
4 7 8 9 6 6 9 7 2 5 7 5 0 6 6 8
8 2 2 3 6 3 6 9 0 7 3 3 2 8 7 5 8
2 2 3 6 0 7 2 0 0 4 4 5 7 5 9 1 9 2
7 0 5 7 3 6 7 0 8 4 7 8 8 0 3 0 2 4 9

15 246
5 0 0 5 1 1 5 3 8 1 4 5 1 8 8
0 3 9 9 2 3 0 3 8 8 5 6 4 1
2 6 9 7 8 6 8 4 7 4 4 1 9
2 3 7 7 5 8 5 5 6 7 0 7
4 2 2 7 8 7 2 5 9 3 3
1 2 1 6 8 4 9 4 6 1
9 4 4 2 3 4 4 5 8
8 1 4 0 8 1 9 7
0 1 4 0 9 0 7
4 7 3 2 5 2
9 0 3 7 0
9 1 4 8
3 3 1
1 5
3
1 5
0 4 1
3 1 2 4
2 6 0 4 6
5 8 1 8 5 8
4 5 4 2 8 6 9
5 7 2 4 9 2 0 4
3 0 3 9 0 7 2 5 8
6 0 5 1 3 5 5 2 5 0
5 6 9 4 0 6 3 7 2 6 9
2 3 4 3 6 9 5 9 1 4 0 9
8 3 3 5 2 1 3 3 3 7 6 0 2
6 7 9 9 9 6 8 8 5 2 4 8 2 7
4 1 2 5 9 7 8 1 0 5 7 2 3 3 9

8 87
5 9 0 1 3 4 7 2
3 6 4 0 2 2 9
6 7 0 9 9 7
8 6 6 3 1
3 9 1 2
4 5 0
7 7
8
9 2
4 9 0
8 0 7 4
2 3 3 2 9
2 1 8 6 6 9
8 0 8 1 1 6 6
6 7 8 6 2 6 5 0

11 176
9 6 1 3 4 5 3 7 4 2 5
8 5 8 4 5 9 1 6 2 4
6 8 8 6 1 8 6 7 5
3 6 9 5 0 8 8 9
0 5 3 9 2 1 5
4 1 4 1 9 0
8 0 6 6 6
4 3 8 7
5 2 5
5 6
8
1 2
2 7 4
7 0 0 6
6 6 0 2 9
6 4 7 5 6 4
6 9 9 9 4 4 7
5 7 1 8 3 1 0 1
6 4 2 6 7 1 5 1 3
8 8 5 2 9 4 2 6 4 6
2 5 1 0 7 0 4 9 8 1 6

3 41
0 1 7
0 1
6
3 3
6 5 1

13 220
5 3 3 5 6 6 7 0 5 3 9 3 5
9 3 2 8 7 8 6 9 1 8 7 8
0 7 6 3 9 6 0 0 8 3 7
9 6 9 2 1 5 2 4 8 3
8 4 3 1 9 7 0 2 7
9 9 4 0 6 7 9 7
8 8 3 6 0 8 3
7 5 7 3 2 3
3 4 5 7 2
1 3 9 3
3 8 7
3 0
0
8 9
6 0 4
9 9 3 4
5 3 1 7 9
7 0 7 8 1 8
5 0 7 2 0 6 3
1 5 4 3 9 0 4 6
4 0 9 0 9 9 4 5 7
8 0 4 7 2 1 8 2 8 0
6 3 8 5 1 7 7 5 7 4 9
6 6 5 0 1 7 4 7 3 9 4 0
4 9 4 7 1 9 6 4 9 9 1 3 9

14 145
6 4 4 4 3 9 9 4 0 9 2 9 2 3
2 7 4 3 7 1 9 9 9 5 9 2 4
6 2 8 9 3 9 3 9 5 2 8 8
4 1 3 0 4 1 0 2 2 2 9
3 6 6 5 0 9 2 2 6 3
0 8 3 0 8 9 2 6 6
9 6 1 5 8 6 2 7
6 4 6 5 5 2 3
6 7 3 0 1 6
9 5 3 2 2
9 6 8 4
0 1 6
3 4
0
7 3
8 4 6
1 6 6 4
1 6 4 8 9
6 0 1 2 2 8
4 9 8 9 5 2 7
9 8 8 6 0 2 0 6
7 3 9 2 5 2 7 3 9
0 7 1 9 1 7 6 1 9 9
1 1 8 5 0 8 5 1 0 7 9
8 3 4 5 9 9 4 9 0 7 1 1
8 9 2 4 5 0 6 3 9 3 0 1 2
3 7 1 3 4 1 3 0 6 1 4 5 4 1

9 113
9 1 4 9 4 9 7 7 1
9 2 8 3 0 3 2 5
2 5 0 6 0 6 4
4 8 9 6 7 4
7 6 8 9 1
7 0 4 6
8 2 0
9 9
0
6 2
4 5 7
0 7 5 2
4 5 3 8 0
2 9 4 6 9 2
3 6 8 9 8 1 5
1 7 0 9 2 0 1 0
5 4 8 9 0 0 3 2 7

4 57
2 7 1 4
0 3 7
6 5
2
1 7
0 6 1
5 2 1 3

0 0

My output is:

Code: Select all

5675
0 RRRRRRRRRRRLRRLRLRRL
18331403
0 RRRRRRRRRRRRRRRLLLLLLLLLLRRLRL
59
14 LLLLLRLRLRRLLLLLLLRRRRRRRRRRRRRRRRRR
703854
4 LRRRRLRLRRRLRRRRRRRRRRRRLRRLRLRLRRRLLL
0

0

17315924
3 RLLRRRRRRRRRRRRRLRRLLRRRRRLLLLLLRRRRLR
0

22
0 RRRRRLLLLL
2
2 LRLLRL
110
1 RRRRLRRLRLRR
0

0

0

1
6 LLLRRLLLRRLRLLLLRRLR
147054
3 RRRRRRRRLRLLRRRRRRRRRRRRRRRRRR
0

51722
4 RRRRRRRRRRLLRRRLLLLLLLLRRRRLRLRLRL
0

0

0

444575
0 RRRRRRRRRRRRRRLLLLLRRRRLLLLR
5
6 RRLRRRRRLLLLLRRRRRRRRRRRRRRR
0

0

0

938
4 RRRRRRRRLLRLRLLLLLRRLLLLLLLL
0

0

0

5810
4 RRRRRLRRRRRRLLLRRRRRRRRRRRRRRRRR
0

0

0

4
2 RLLRLRLR
3058355
0 RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
0

0

0

527914
0 RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
0

0

0

6462
1 RRRRRRRRRRRLRLLLLLLRRLLRRL
0

387866994
0 RRRRRRRRRRRRRRRRRLLLLLLLLLLLLRRRRL
0

0

20
0 RRRRRRLRRLLL
0

432226083
0 RRRRRRRRRRRRRRRRRRLLLLLLLLLRLLLRLLRL
2090726
1 RRRRRRRRRRRRRRLRRRRRRRRRRRRRRRRRRRRR
0

0

0

50
4 RRLLRLRLRLLLLRRLLR
0

0

1955331
0 RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
0

0

7827
0 RRRRRRRRRLLLRRLLLR
0

0

1757070
0 RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
0

0

0

49
0 RRRRRLLRLR
0

10663
7 RRRLRRRLLRRLRRLLLRLRLLLRLLLLLLLLRRRR
22
1 RRRRRRRRRRRLRRRRRRRRRRRRRRRR
188
0 RRRRRRRLRLLRLR
0

0

0

149616
0 RRRRRRRRRRRRRLLRLLLLRRLRLR
19
0 RRRRRRRRLRLLLRRL
0

Is this the same as yours? Thanks.

[Martin Macko]

My AC's output is:

Code: Select all

5675
0 RRRRRRRRRRRLRRLRLRRL
18331403
0 RRRRRRRRRRRRRRRLLLLLLLLLLRRLRL
0

703854
4 LRRRRLRLRRRLRRRRRRRRRRRRLRRLRLRLRRRLLL
0

0

17315924
3 RLLRRRRRRRRRRRRRLRRLLRRRRRLLLLLLRRRRLR
0

22
0 RRRRRLLLLL
2
2 LRLLRL
110
1 RRRRLRRLRLRR
0

0

0

1
6 LLLRRLLLRRLRLLLLRRLR
0

0

51722
4 RRRRRRRRRRLLRRLLRLLLLLLRRRRLRRRLLL
0

0

0

444575
0 RRRRRRRRRRRRRRLLLLLRRRRLLLLR
0

0

0

0

938
4 RRRRRRRRLLRLRLLLLLRRLLLLLLLL
0

0

0

0

0

0

0

4
2 RLLRLRLR
0

0

0

0

0

0

0

0

6462
1 RRRRRRRRRRRLRLLLLLLRRLLRRL
0

387866994
0 RRRRRRRRRRRRRRRRRLLLLLLLLLLLLRRRRL
0

0

20
0 RRRRRRLRRLLL
0

432226083
0 RRRRRRRRRRRRRRRRRRLLLLLLLLLRLLLRLLRL
0

0

0

0

50
4 RRLLRLRLRLLLLRRLLR
0

0

0

0

0

7827
0 RRRRRRRRRLLLRRLLLR
0

0

0

0

0

0

49
0 RRRRRLLRLR
0

10663
7 RLRRRRRLLRLRRRLLLRLRLLLRLRRRRRRRRRRL
0

188
0 RRRRRRRLRLLRLR
0

0

0

149616
0 RRRRRRRRRRRRRLLRLLLLRRLRLR
19
0 RRRRRRRRLRLLLRRL
0

[ImLazy]

Thank you, Martin Macko.Now my programe have the exactly same output with you. But still WA. I'm getting crazy.

[ImLazy]

Dear Martin Macko, can you give me your output for this input data? Thanks.
http://baidiheizi.diy.myrice.com/bbs/in.txt
There are 1000 cases in this input file.

[Martin Macko]

Dear Martin Macko, can you give me your output for this input data? Thanks.

The inputs and outputs are (gzipped) at http://www.ksp.sk/~martin/val/10564/

good luck

[ImLazy]

The same output as yours and still WA.
I think I should give it up now.
Thank you anyway, Martin Macko.

[Martin Macko]

The same output as yours and still WA.
I think I should give it up now.
Thank you anyway, Martin Macko.

Well... have you (double)checked all special cases? N=2; N=20; S=0; All cells with the same value; Or write a bruteforce for small N and compare the outputs for all possible inputs (for small N).

If nothing helps, post your code here... If I'll have time I'll look at it...

[ImLazy]

Dear Martin Macko, I've got AC!
I used to divide the hourglass into two pyramids, the top one and the bottom one, and count the paths respectively. Because I thought this can be faster. But this method complicate the problem and caused WA.
Today I retyped my code and this time I didn't divide the hourglass. Soon I got AC.
Thank you for giving me so much help.

[Martin Macko]

Dear Martin Macko, I've got AC!
I used to divide the hourglass into two pyramids, the top one and the bottom one, and count the paths respectively. Because I thought this can be faster. But this method complicate the problem and caused WA.
Today I retyped my code and this time I didn't divide the hourglass. Soon I got AC.
Thank you for giving me so much help.

Could you, please, delete the wrong outputs to make sure we won't confuse somebody?

[zslwyuan]

I have gotten Wrong, However , I can't find the mistake, Please help me Check The Code?
My Idea: First I use the DP to get the sum of the paths, Then, I use the DFS to find out the best path.
==========================================>>I got Wrong Answer

Help!

#include<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>
using namespace std;
int map[25][25];
int f[42][42][502];
int g,s,n;
char ss[100];
int ll;
void dfs(int x,int y,int u,int be)
{
if (map[x][y]<0)return;
if (x==2*n-1&&u==s) {printf("%d ",be-1);g=1;return;}
if (x==2*n-1||(x<2*n-1&&u>s))return;
if (x<n)
{
{dfs(x+1,y-1,u+map[x+1][y-1],be); if (g){ss[x]='L';;return;}}
{dfs(x+1,y,u+map[x+1][y],be); if (g){ss[x]='R';return;}}
}
else
{
{dfs(x+1,y,u+map[x+1][y],be); if (g){ss[x]='L';return;}}
{dfs(x+1,y+1,u+map[x+1][y+1],be); if (g){ss[x]='R';return;}}
}
}

int main()
{
freopen("1.txt","r",stdin);
freopen("2.txt","w",stdout);
int i,j,k,l,m;
while (scanf("%d%d",&n,&s))
{
if (n==0) break;
memset(map,-1,sizeof(map));
memset(f,0,sizeof(f));
for (i=1;i<=n;i++)
for (j=1;j<=n-i+1;j++)
scanf("%d",&map[j]);
for (i=1+n;i<=n+n-1;i++)
for (j=1;j<=i-n+1;j++)
scanf("%d",&map[j]);
memset(f[1],0,sizeof(f[1]));
for (i=1;i<=n;i++)
if (map[1]>=0)
f[1][map[1]]=1;
for (i=2;i<=n;i++)
for (j=1;j<=n;j++)
{
if (map[j]<0) break;
for(k=s;k>=0;k--)
{
f[j][k]=0;
if (k>map[j])
{
int g1=0,g2=0;
g1=f[i-1][j][k-map[j]];
g2=f[i-1][j+1][k-map[j]];
if (map[i][j]>=0)
f[i][j][k]+=(g1+g2);
}else break;
}
}
for (i=n+1;i<=2*n-1;i++)
for (j=1;j<=n;j++)
{
if (map[i][j]<0) break;
for(k=s;k>=0;k--)
{
f[i][j][k]=0;
if (k>map[i][j])
{
int g1=0,g2=0;
g1=f[i-1][j][k-map[i][j]];
g2=f[i-1][j-1][k-map[i][j]];
if (map[i][j]>=0)
f[i][j][k]+=(g1+g2);
}else break;
}
}
int sum=0;
for (i=1;i<=n;i++)
sum+=f[2*n-1][i][s];
printf("%d\n",sum);
if (sum)
{
memset(ss,0,sizeof(s));
g=0;
for (i=1;i<=n;i++)
{dfs(1,i,map[1][i],i);if(g)break;}
int len=strlen(ss);
if (g) for (i=1;i<=2*n-2;i++)printf("%c",ss[i]);
}
printf("\n");
}
return 0;
}

[CSGrandeur]

????long long