Problem Statement

You are given a sequence of M integers A = (A_1, A_2, \dots, A_M).
Each element of A is an integer between 1 and N, inclusive, and all elements are distinct.

List all integers between 1 and N that do not appear in A in ascending order.

Constraints

• All input values are integers.
• 1 \le M \le N \le 1000
• 1 \le A_i \le N
• The elements of A are distinct.

Sample Input 1

10 3
3 9 2

Sample Output 1

7
1 4 5 6 7 8 10

Here, A=(3,9,2).
The integers between 1 and 10 that do not appear in A, listed in ascending order, are 1,4,5,6,7,8,10.

Sample Input 2

6 6
1 3 5 2 4 6

Sample Output 2

0

No integer between 1 and 6 is missing from A.
In this case, print 0 on the first line and leave the second line empty.

Sample Input 3

9 1
9

Sample Output 3

8
1 2 3 4 5 6 7 8

Problem Statement

Given an integer X between -10^{18} and 10^{18} (inclusive), print \left\lfloor \dfrac{X}{10} \right\rfloor.

Notes

For a real number x, \left\lfloor x \right\rfloor denotes "the maximum integer not exceeding x". For example, we have \left\lfloor 4.7 \right\rfloor = 4, \left\lfloor -2.4 \right\rfloor = -3, and \left\lfloor 5 \right\rfloor = 5. (For more details, please refer to the description in the Sample Input and Output.)

Constraints

• -10^{18} \leq X \leq 10^{18}
• All values in input are integers.

Sample Input 1

47

Sample Output 1

4

The integers that do not exceed \frac{47}{10} = 4.7 are all the negative integers, 0, 1, 2, 3, and 4. The maximum integer among them is 4, so we have \left\lfloor \frac{47}{10} \right\rfloor = 4.

Sample Input 2

-24

Sample Output 2

-3

Since the maximum integer not exceeding \frac{-24}{10} = -2.4 is -3, we have \left\lfloor \frac{-24}{10} \right\rfloor = -3.
Note that -2 does not satisfy the condition, as -2 exceeds -2.4.

Sample Input 3

50

Sample Output 3

5

The maximum integer that does not exceed \frac{50}{10} = 5 is 5 itself. Thus, we have \left\lfloor \frac{50}{10} \right\rfloor = 5.

Sample Input 4

-30

Sample Output 4

-3

Just like the previous example, \left\lfloor \frac{-30}{10} \right\rfloor = -3.

Sample Input 5

987654321987654321

Sample Output 5

98765432198765432

The answer is 98765432198765432. Make sure that all the digits match.

If your program does not behave as intended, we recommend you checking the specification of the programming language you use.
If you want to check how your code works, you may use "Custom Test" above the Problem Statement.

Problem Statement

Takahashi is on a two-dimensional plane. Starting from the origin, he made N moves.

The N moves are represented by a string of length N as described below:

• Takahashi's coordinates after the i-th move are:

  • (x+1,y) if the i-th character of S is R;
  • (x-1,y) if the i-th character of S is L;
  • (x,y+1) if the i-th character of S is U; and
  • (x,y-1) if the i-th character of S is D,

  where (x,y) is his coordinates before the move.

Determine if Takahashi visited the same coordinates multiple times in the course of the N moves (including the starting and ending points).

Constraints

• 1 \leq N \leq 2\times 10^5
• N is an integer.
• S is a string of length N consisting of R, L, U, and D.

Sample Input 1

5
RLURU

Sample Output 1

Yes

Takahashi's coordinates change as follows: (0,0)\to (1,0)\to (0,0)\to (0,1)\to (1,1)\to (1,2).

Sample Input 2

20
URDDLLUUURRRDDDDLLLL

Sample Output 2

No

Problem Statement

There is an N\times N grid with horizontal rows and vertical columns, where all squares are initially painted white. Let (i,j) denote the square at the i-th row and j-th column.

Takahashi has integers A and B, which are between 1 and N (inclusive). He will do the following operations.

• For every integer k such that \max(1-A,1-B)\leq k\leq \min(N-A,N-B), paint (A+k,B+k) black.
• For every integer k such that \max(1-A,B-N)\leq k\leq \min(N-A,B-1), paint (A+k,B-k) black.

In the grid after these operations, find the color of each square (i,j) such that P\leq i\leq Q and R\leq j\leq S.

Constraints

• 1 \leq N \leq 10^{18}
• 1 \leq A \leq N
• 1 \leq B \leq N
• 1 \leq P \leq Q \leq N
• 1 \leq R \leq S \leq N
• (Q-P+1)\times(S-R+1)\leq 3\times 10^5
• All values in input are integers.

Sample Input 1

5 3 2
1 5 1 5

Sample Output 1

...#.
#.#..
.#...
#.#..
...#.

The first operation paints the four squares (2,1), (3,2), (4,3), (5,4) black, and the second paints the four squares (4,1), (3,2), (2,3), (1,4) black.
Thus, the above output should be printed, since P=1, Q=5, R=1, S=5.

Sample Input 2

5 3 3
4 5 2 5

Sample Output 2

#.#.
...#

The operations paint the nine squares (1,1), (1,5), (2,2), (2,4), (3,3), (4,2), (4,4), (5,1), (5,5).
Thus, the above output should be printed, since P=4, Q=5, R=2, S=5.

Sample Input 3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Sample Output 3

#.#
.#.
#.#

Note that the input may not fit into a 32-bit integer type.

Problem Statement

There is an infinitely large two-dimensional grid, with a campfire at coordinate (0,0).
At time t=0, smoke exists only at cell (0,0).

You are given a length-N string S consisting of N, W, S, E. At times t=1,2,\dots,N, the following happen in order:

• Wind blows, and all the smoke present at that time moves as follows:
  • If the t-th character of S is N, smoke in cell (r,c) moves to cell (r-1,c).
  • If it is W, smoke in cell (r,c) moves to cell (r,c-1).
  • If it is S, smoke in cell (r,c) moves to cell (r+1,c).
  • If it is E, smoke in cell (r,c) moves to cell (r,c+1).
• If there is no smoke in cell (0,0), new smoke is generated at cell (0,0).

Takahashi is standing at cell (R,C).
For each integer 1 \le t \le N, determine if smoke exists at cell (R,C) at time t+0.5, and print the response according to the required format.

Constraints

• N is an integer between 1 and 200000, inclusive.
• S is a length N string consisting of N, W, S, E.
• R and C are integers between -N and N, inclusive.
• (R,C) \neq (0,0)

Sample Input 1

6 -2 1
NNEEWS

Sample Output 1

001010

At times 1.5,2.5,4.5,6.5, there is no smoke at cell (-2,1). At times 3.5,5.5, there is smoke at cell (-2,1).
Hence, output 001010.

In the figures below, taking cell (0,0) with the campfire as a reference, cell (r,c) is drawn:

• -r cells up if r < 0,
• r cells down if r \ge 0,
• -c cells left if c < 0,
• c cells right if c \ge 0.

The grid at time 0.5 looks like:

The grid at time 1.5 looks like:

The grid at time 2.5 looks like:

The grid at time 3.5 looks like:

The grid at time 4.5 looks like:

The grid at time 5.5 looks like:

The grid at time 6.5 looks like:

Sample Input 2

10 1 2
NEESESWEES

Sample Output 2

0001101011

Sample Input 3

20 -1 -2
WWNNWSWEWNSWWENSNWWN

Sample Output 3

00100111111000101111