Problem Statement

The magnitude of an earthquake is a logarithmic scale of the energy released by the earthquake. It is known that each time the magnitude increases by 1, the amount of energy gets multiplied by approximately 32.
Here, we assume that the amount of energy gets multiplied by exactly 32 each time the magnitude increases by 1. In this case, how many times is the amount of energy of a magnitude A earthquake as much as that of a magnitude B earthquake?

Constraints

• 3\leq B\leq A\leq 9
• A and B are integers.

Sample Input 1

6 4

Sample Output 1

1024

6 is 2 greater than 4, so a magnitude 6 earthquake has 32\times 32=1024 times as much energy as a magnitude 4 earthquake has.

Sample Input 2

5 5

Sample Output 2

1

Earthquakes with the same magnitude have the same amount of energy.

Problem Statement

Assuming that the horizon seen from a place x meters above the ground is \sqrt{x(12800000+x)} meters away, find how many meters away the horizon seen from a place H meters above the ground is.

Constraints

• 1 \leq H \leq 10^5
• H is an integer.

Sample Input 1

333

Sample Output 1

65287.907678222

We have \sqrt{333(12800000+333)} = 65287.9076782\ldots. Outputs such as 65287.91 would also be accepted.

Sample Input 2

634

Sample Output 2

90086.635834623

We have \sqrt{634(12800000+634)} = 90086.6358346\ldots.

Problem Statement

There are N people. The family name and given name of the i-th person (1 \leq i \leq N) are S_i and T_i, respectively.

Determine whether there is a pair of people with the same family and given names. In other words, determine whether there is a pair of integers (i,j) such that 1 \leq i \lt j \leq N, S_i=S_j, and T_i=T_j.

Constraints

• 2 \leq N \leq 1000
• N is an integer.
• Each of S_i and T_i is a string of length between 1 and 10 (inclusive) consisting of English lowercase letters.

Sample Input 1

3
tanaka taro
sato hanako
tanaka taro

Sample Output 1

Yes

The first and third persons have the same family and given names.

Sample Input 2

3
saito ichiro
saito jiro
saito saburo

Sample Output 2

No

No two persons have the same family and given names.

Sample Input 3

4
sypdgidop bkseq
bajsqz hh
ozjekw mcybmtt
qfeysvw dbo

Sample Output 3

No

Problem Statement

There are N competitive programmers numbered person 1, person 2, \ldots, and person N.
There is a relation called superiority between the programmers. For all pairs of distinct programmers (person X, person Y), exactly one of the following two relations holds: "person X is stronger than person Y" or "person Y is stronger than person X."
The superiority is transitive. In other words, for all triplets of distinct programmers (person X, person Y, person Z), it holds that:

• if person X is stronger than person Y and person Y is stronger than person Z, then person X is stronger than person Z.

A person X is said to be the strongest programmer if person X is stronger than person Y for all people Y other than person X. (Under the constraints above, we can prove that there is always exactly one such person.)

You have M pieces of information on their superiority. The i-th of them is that "person A_i is stronger than person B_i."
Can you determine the strongest programmer among the N based on the information?
If you can, print the person's number. Otherwise, that is, if there are multiple possible strongest programmers, print -1.

Constraints

• 2 \leq N \leq 50
• 0 \leq M \leq \frac{N(N-1)}{2}
• 1 \leq A_i, B_i \leq N
• A_i \neq B_i
• If i \neq j, then (A_i, B_i) \neq (A_j, B_j).
• There is at least one way to determine superiorities for all pairs of distinct programmers, that is consistent with the given information.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

1

You have two pieces of information: "person 1 is stronger than person 2" and "person 2 is stronger than person 3."
By the transitivity, you can also infer that "person 1 is stronger than person 3," so person 1 is the strongest programmer.

Sample Input 2

3 2
1 3
2 3

Sample Output 2

-1

Both person 1 and person 2 may be the strongest programmer. Since you cannot uniquely determine which is the strongest, you should print -1.

Sample Input 3

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

Sample Output 3

-1

Problem Statement

There are zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row from the top and the j-th column from the left.
Whether each square contains a sensor is given by the strings S_1, S_2, \ldots, S_H, each of length W. (i, j) contains a sensor if and only if the j-th character of S_i is #.
These sensors interact with other sensors in the squares horizontally, vertically, or diagonally adjacent to them and operate as one sensor. Here, a cell (x, y) and a cell (x', y') are said to be horizontally, vertically, or diagonally adjacent if and only if \max(|x-x'|,|y-y'|) = 1.
Note that if sensor A interacts with sensor B and sensor A interacts with sensor C, then sensor B and sensor C also interact.

Considering the interacting sensors as one sensor, find the number of sensors on this grid.

Constraints

• 1 \leq H, W \leq 1000
• H and W are integers.
• S_i is a string of length W where each character is # or ..

Sample Input 1

5 6
.##...
...#..
....##
#.#...
..#...

Sample Output 1

3

When considering the interacting sensors as one sensor, the following three sensors exist:

• The interacting sensors at (1,2),(1,3),(2,4),(3,5),(3,6)
• The sensor at (4,1)
• The interacting sensors at (4,3),(5,3)

Sample Input 2

3 3
#.#
.#.
#.#

Sample Output 2

1

Sample Input 3

4 2
..
..
..
..

Sample Output 3

0

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

7