TEST DATA FOR `patterns'

Input for test 1

8 2
1
2
3
2
3
2
3
1

Output for test 1

4

Input for test 2

10 2
3
3
3
4
2
2
2
4
2
2

Output for test 2

3

Input for test 3

20 2
3
3
3
2
2
2
3
3
3
2
2
3
3
1
2
3
2
3
2
3

Output for test 3

5

Input for test 4

30 2
5
5
6
11
4
4
2
7
7
12
6
12
3
1
1
6
5
7
9
5
2
6
11
11
3
12
9
6
9
3

Output for test 4

2

Input for test 5

40 2
2
3
3
5
4
6
4
5
2
4
6
4
5
1
1
4
5
3
4
6
6
4
5
2
3
2
4
4
3
2
6
5
5
3
4
6
3
6
5
4

Output for test 5

4

Input for test 6

1000 15
1
1
1
1
1
1
1
1
1
1
1
1
13
1
8
1
1
1
1
1
1
20
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
20
1
1
1
1
1
1
1
1
1
1
1
12
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23
4
5
1
3
6
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
16
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
5
1
1
1
1
1
1
1
1
1
1
1
12
1
1
1
1
1
18
1
1
1
1
1
1
1
1
1
1
1
12
1
1
1
1
1
9
1
1
1
1
1
1
1
1
20
1
1
1
1
1
1
1
1
1
1
1
1
17
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
7
1
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
22
1
1
1
1
1
1
1
22
1
1
1
1
11
1
1
1
1
19
1
1
1
1
1
1
1
1
21
1
1
1
1
1
1
1
14
1
1
1
1
1
15
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
4
1
1
12
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
13
1
1
1
1
1
1
18
1
1
23
1
1
1
1
1
1
1
1
15
6
1
1
11
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
14
1
1
1
1
1
1
1
23
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
13
8
1
1
1
1
13
1
17
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
13
1
1
1
1
1
1
1
1
8
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
6
4
1
1
1
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
9
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
1
11
1
1
1
1
5
1
1
3
1
21
1
1
1
1
1
20
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
16
1
1
1
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
16
1
1
1
1
12
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
11
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
17
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
13
1
1
1
1
1
21
1
1
1
1
1
1
1
1
1
1
23
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
17
1
13
1
22
1
1
1
1
18
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1

Output for test 6

32

Input for test 7

1000 12
3
3
3
1
1
1
1
1
1
5
1
6
3
1
1
1
1
2
6
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
4
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
6
6
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
5
4
3
1
3
2
1
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
7
1
1
1
1
1
1
1
2
5
2
4
1
5
1
1
1
1
1
3
1
1
1
1
1
1
1
1
5
5
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
1
2
1
6
1
4
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
1
1
2
2
1
4
1
1
1
1
1
1
7
1
1
5
1
1
1
1
1
1
6
1
6
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
5
1
2
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
6
1
4
1
1
1
1
4
1
2
1
1
1
2
1
1
1
1
1
4
1
1
2
1
1
1
4
6
1
1
5
1
1
1
1
7
1
1
1
1
1
1
1
1
3
4
1
4
1
1
6
1
1
1
1
1
3
1
2
1
1
1
3
1
1
1
1
6
1
1
1
6
2
1
1
2
1
1
1
1
1
5
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
5
1
1
1
3
6
1
1
1
1
2
1
1
3
1
3
1
1
1
1
6
2
1
2
7
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
6
1
1
4
1
1
1
3
1
1
6
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
2
1
1
1
1
7
1
3
1
1
6
1
1
1
1
1
5
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
7
3
1
1
1
1
1
1
1
1
2
5
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
7
2
6
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
7
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
5
1
1
1
1
7
1
1
5
1
3
6
1
1
1
2
1
4
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
4
1
1
1
4
1
1
1
3
1
1
1
1
1
1
1
4
1
1
1
5
1
1
1
1
1
5
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
6
5
1
1
1
1
1
7
1
1
1
4
1
7
1
7
1
1
7
1
1
1
1
1
6
1
1
1
3
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
5
1
1
1
1
5
1
1
1
1
1
1
7
1
1
1
1
2
1
1
1
1
1
1
1
6
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
5
7
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
3
6
6
1
1
1
2
1
1
1
1
1
4
3
1
1
7
1
1
7
1
1
4
1
1
1
1
1
1
1
1
1
3
1
1
1
4
5
1
1
1
1
1
1
4
3
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
3
1
5
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
5
1
1
2
1
1
1
1
1
3
1
5
1
1
1
1
7
4
1
2
7
6
1
6
1
1
1
1
1
5
1
1
1
1
4
1
1
1
1

Output for test 7

19

Input for test 8

1000 3
3
9
3
1
1
2
8
8
1
9
6
1
1
1
5
2
1
1
1
1
1
1
5
1
1
3
1
1
4
8
1
7
1
1
1
4
1
1
1
1
1
1
1
4
1
1
6
3
1
1
1
6
1
1
1
1
2
6
1
5
9
6
3
1
1
1
3
6
1
1
1
8
7
1
1
2
7
9
1
9
2
9
7
1
2
4
1
1
1
1
1
1
1
7
1
1
4
1
9
1
1
10
1
1
4
1
1
1
8
8
8
4
1
5
1
2
6
6
1
1
1
8
1
1
5
1
8
1
5
9
1
6
1
6
5
9
1
2
5
1
2
1
6
1
10
6
2
7
1
1
10
1
1
10
1
9
2
5
5
6
10
1
1
1
1
2
2
1
5
2
1
1
6
6
1
3
1
1
1
1
9
4
1
1
6
1
1
1
1
3
1
7
10
4
2
1
2
1
5
1
1
1
1
1
1
1
3
1
1
1
5
9
1
4
1
1
1
2
8
8
1
1
1
8
1
1
1
8
10
2
8
1
1
1
7
6
1
1
5
4
1
5
2
9
10
1
4
9
10
10
1
1
1
6
1
3
4
9
1
5
1
4
6
1
1
1
2
1
10
1
6
5
1
1
8
1
6
9
8
1
1
1
1
1
1
1
1
5
6
1
1
1
1
1
1
1
1
2
2
2
5
1
1
1
6
3
3
1
1
5
3
3
3
6
5
9
5
3
8
10
1
1
4
1
1
10
2
1
1
1
5
7
1
8
1
9
1
1
7
1
7
6
1
5
8
7
1
1
5
1
9
1
9
9
9
1
8
1
1
4
3
9
1
1
1
10
1
3
4
6
1
6
1
9
1
1
1
7
1
1
1
9
5
1
1
6
1
7
1
1
1
1
1
1
1
9
10
9
1
1
6
1
1
1
1
5
8
1
1
1
8
6
5
1
1
1
1
1
1
10
1
1
8
4
2
6
7
6
1
9
2
1
1
5
3
1
1
1
5
1
1
3
7
6
1
6
6
2
5
10
2
1
10
9
1
9
4
6
1
1
1
6
8
1
1
6
1
5
6
1
3
1
1
10
9
2
1
1
1
7
1
1
4
2
1
1
1
9
1
5
1
1
1
1
1
6
1
1
1
1
1
1
10
1
1
8
1
1
1
1
4
1
7
1
1
3
9
3
7
1
1
7
1
1
1
1
7
1
1
1
9
6
3
6
1
6
1
4
10
4
1
9
4
1
1
1
3
1
9
1
1
9
4
1
1
2
1
1
1
10
1
5
5
1
1
1
5
1
4
9
1
1
4
1
9
2
8
1
9
9
2
1
1
1
1
1
7
1
7
10
9
3
7
1
1
7
1
7
1
2
3
1
4
1
1
1
3
1
1
1
1
1
1
1
1
5
7
1
8
7
1
10
1
10
10
5
1
8
1
1
1
4
6
8
1
1
1
7
1
1
6
2
1
2
1
1
3
3
7
1
5
2
8
8
1
1
4
4
1
1
1
5
9
9
2
8
10
1
1
9
1
7
10
10
1
2
1
3
7
1
10
5
7
1
1
1
1
1
1
1
3
2
6
6
3
1
10
8
2
2
1
4
3
1
1
10
1
8
4
1
10
1
1
10
1
1
1
1
1
3
2
1
10
5
1
10
5
1
10
3
7
8
1
7
5
1
1
1
1
1
1
1
1
1
3
1
8
5
5
1
1
5
1
1
1
8
1
1
1
1
1
5
3
4
1
2
6
1
1
2
5
1
1
4
7
1
5
8
1
7
1
5
5
9
1
1
5
1
1
4
4
4
1
8
4
6
7
1
1
1
1
8
8
1
1
9
10
10
1
10
6
9
1
1
7
1
6
3
1
6
1
9
10
1
1
1
8
6
8
6
7
1
3
1
4
2
2
1
9
2
1
1
1
4
3
1
3
1
10
1
9
3
6
9
8
1
1
1
10
5
4
1
3
5
7
1
9
1
4
6
1
4
1
1
4
10
1
1
1
1
1
8
3
1
1
2
2
3
1
10
10
1
8
1
3
1
6
2
1
1
1
1
3
1
1
10
1
1
1
9
1
3
1
1
1
3
1
3
10
1
1
7
5
1
9
7
10
1
1
1
1
2
1
1
3
10
1
1
1
3
4
1
1
9
1
2
2
5
1
1
1
1
10
8
9
1
1
10
1
1
1
1
8
1
1
4
9
1
1
7
1
9
7
3
1
1
1
9
2
6
1
1
6
8
4
1
1
5
7
1
5
10
1
1
1
4
6
1
3
1

Output for test 8

8

Input for test 9

10000 42
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
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1
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1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
1
1
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1
1
1
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1
1
1
1
1
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1
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1
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1
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1
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1
1
1
1
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1
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1
1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
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1
1
1
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1
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1
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1
1
1
1
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1
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1
1
1
1
1
1
1
2
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1
1
1
1
1
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1
1
1
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1
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1
1
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1
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1
1
1
1
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1
1
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1
1
1
1
1
1
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1
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1
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1
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1
1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Output for test 9

103

Input for test 10

20000 2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Output for test 10

1042