alexjercan/bugnet huggingface dataset:
Score : 800 points

Problem Statement

There are N towns in Snuke Kingdom, conveniently numbered 1 through N.
Town 1 is the capital.

Each town in the kingdom has a Teleporter, a facility that instantly transports a person to another place.
The destination of the Teleporter of town i is town a_i (1≤a_i≤N).
It is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.

King Snuke loves the integer K.
The selfish king wants to change the destination of the Teleporters so that the following holds:

Starting from any town, one will be at the capital after using the Teleporters exactly K times in total.

Find the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.

Constraints

2≤N≤10^5

1≤a_i≤N

One can get to the capital from any town by using the Teleporters some number of times.

1≤K≤10^9

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.

Sample Input 1

3 1
2 3 1

Sample Output 1

2

Change the destinations of the Teleporters to a = (1,1,1).

Sample Input 2

4 2
1 1 2 2

Sample Output 2

0

There is no need to change the destinations of the Teleporters, since the king's desire is already satisfied.

Sample Input 3

8 2
4 1 2 3 1 2 3 4

Sample Output 3

3

For example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4).
Score : 1400 points

Problem Statement

We have a grid with H rows and W columns.
The state of the cell at the i-th (1≤i≤H) row and j-th (1≤j≤W) column is represented by a letter a_{ij}, as follows:

. : This cell is empty.

o : This cell contains a robot.

E : This cell contains the exit. E occurs exactly once in the whole grid.

Snuke is trying to salvage as many robots as possible, by performing the following operation some number of times:

Select one of the following directions: up, down, left, right. All remaining robots will move one cell in the selected direction, except when a robot would step outside the grid, in which case the robot will explode and immediately disappear from the grid. If a robot moves to the cell that contains the exit, the robot will be salvaged and immediately removed from the grid.

Find the maximum number of robots that can be salvaged.

Constraints

2≤H,W≤100

a_{ij} is ., o or E.

E occurs exactly once in the whole grid.

Input

The input is given from Standard Input in the following format:

H W
a_{11}...a_{1W}
:
a_{H1}...a_{HW}

Output

Print the maximum number of robots that can be salvaged.

Sample Input 1

3 3
o.o
.Eo
ooo

Sample Output 1

3

For example, select left, up, right.

Sample Input 2

2 2
E.
..

Sample Output 2

0

Sample Input 3

3 4
o...
o...
oooE

Sample Output 3

5

Select right, right, right, down, down.

Sample Input 4

5 11
ooo.ooo.ooo
o.o.o...o..
ooo.oE..o..
o.o.o.o.o..
o.o.ooo.ooo

Sample Output 4

12
Score : 2200 points

Problem Statement

You are given an undirected graph with N vertices and M edges.
Here, N-1≤M≤N holds and the graph is connected.
There are no self-loops or multiple edges in this graph.

The vertices are numbered 1 through N, and the edges are numbered 1 through M.
Edge i connects vertices a_i and b_i.

The color of each vertex can be either white or black.
Initially, all the vertices are white.
Snuke is trying to turn all the vertices black by performing the following operation some number of times:

Select a pair of adjacent vertices with the same color, and invert the colors of those vertices. That is, if the vertices are both white, then turn them black, and vice versa.

Determine if it is possible to turn all the vertices black. If the answer is positive, find the minimum number of times the operation needs to be performed in order to achieve the objective.

Constraints

2≤N≤10^5

N-1≤M≤N

1≤a_i,b_i≤N

There are no self-loops or multiple edges in the given graph.

The given graph is connected.

Partial Score

In the test set worth 1500 points, M=N-1.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to turn all the vertices black, print the minimum number of times the operation needs to be performed in order to achieve the objective.
Otherwise, print -1 instead.

Sample Input 1

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

Sample Output 1

5

For example, it is possible to perform the operations as shown in the following diagram:

Sample Input 2

3 2
1 2
2 3

Sample Output 2

-1

It is not possible to turn all the vertices black.

Sample Input 3

4 4
1 2
2 3
3 4
4 1

Sample Output 3

2

This case is not included in the test set for the partial score.

Sample Input 4

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

Sample Output 4

7

This case is not included in the test set for the partial score.
Score : 100 points

Problem Statement

There is a hotel with the following accommodation fee:

X yen (the currency of Japan) per night, for the first K nights

Y yen per night, for the (K+1)-th and subsequent nights

Tak is staying at this hotel for N consecutive nights.
Find his total accommodation fee.

Constraints

1 \leq N, K \leq 10000

1 \leq Y < X \leq 10000

N,\,K,\,X,\,Y are integers.

Input

The input is given from Standard Input in the following format:

N
K
X
Y

Output

Print Tak's total accommodation fee.

Sample Input 1

5
3
10000
9000

Sample Output 1

48000

The accommodation fee is as follows:

10000 yen for the 1-st night

10000 yen for the 2-nd night

10000 yen for the 3-rd night

9000 yen for the 4-th night

9000 yen for the 5-th night

Thus, the total is 48000 yen.

Sample Input 2

2
3
10000
9000

Sample Output 2

20000
Score : 200 points

Problem Statement

Let w be a string consisting of lowercase letters.
We will call w beautiful if the following condition is satisfied:

Each lowercase letter of the English alphabet occurs even number of times in w.

You are given the string w. Determine if w is beautiful.

Constraints

1 \leq |w| \leq 100

w consists of lowercase letters (a-z).

Input

The input is given from Standard Input in the following format:

w

Output

Print Yes if w is beautiful. Print No otherwise.

Sample Input 1

abaccaba

Sample Output 1

Yes

a occurs four times, b occurs twice, c occurs twice and the other letters occur zero times.

Sample Input 2

hthth

Sample Output 2

No
Score : 300 points

Problem Statement

Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i.
He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.
In how many ways can he make his selection?

Constraints

1 \leq N \leq 50

1 \leq A \leq 50

1 \leq x_i \leq 50

N,\,A,\,x_i are integers.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

Input

The input is given from Standard Input in the following format:

N A
x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.
Score : 500 points

Problem Statement

For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:

f(b,n) = n, when n < b

f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b

Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b,
and n \ {\rm mod} \ b denotes the remainder of n divided by b.

Less formally, f(b,n) is equal to the sum of the digits of n written in base b.
For example, the following hold:

f(10,\,87654)=8+7+6+5+4=30

f(100,\,87654)=8+76+54=138

You are given integers n and s.
Determine if there exists an integer b (b \geq 2) such that f(b,n)=s.
If the answer is positive, also find the smallest such b.

Constraints

1 \leq n \leq 10^{11}

1 \leq s \leq 10^{11}

n,\,s are integers.

Input

The input is given from Standard Input in the following format:

n
s

Output

If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b.
If such b does not exist, print -1 instead.

Sample Input 1

87654
30

Sample Output 1

10

Sample Input 2

87654
138

Sample Output 2

100

Sample Input 3

87654
45678

Sample Output 3

-1

Sample Input 4

31415926535
1

Sample Output 4

31415926535

Sample Input 5

1
31415926535

Sample Output 5

-1
Score : 700 points

Problem Statement

N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.

Tak the traveler has the following two personal principles:

He never travels a distance of more than L in a single day.

He never sleeps in the open. That is, he must stay at a hotel at the end of a day.

You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j.
For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.
It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.

Constraints

2 \leq N \leq 10^5

1 \leq L \leq 10^9

1 \leq Q \leq 10^5

1 \leq x_i < x_2 < ... < x_N \leq 10^9

x_{i+1} - x_i \leq L

1 \leq a_j,b_j \leq N

a_j \neq b_j

N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.

Partial Score

200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q

Output

Print Q lines.
The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.

Sample Input 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

4
2
1
2

For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:

Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.

Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.

Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.

Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.
Score : 900 points

Problem Statement

Let x be a string of length at least 1.
We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x.
For example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.

Let w be a string of length at least 1.
For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements,
we will call F a good representation of w, if the following conditions are both satisfied:

For any i \, (1 \leq i \leq m), f_i is a good string.

The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w.

For example, when w=aabb, there are five good representations of w:

(aabb)

(a,abb)

(aab,b)

(a,ab,b)

(a,a,b,b)

Among the good representations of w, the ones with the smallest number of elements are called the best representations of w.
For example, there are only one best representation of w=aabb: (aabb).

You are given a string w. Find the following:

the number of elements of a best representation of w

the number of the best representations of w, modulo 1000000007 \, (=10^9+7)

(It is guaranteed that a good representation of w always exists.)

Constraints

1 \leq |w| \leq 500000 \, (=5 \times 10^5)

w consists of lowercase letters (a-z).

Partial Score

400 points will be awarded for passing the test set satisfying 1 \leq |w| \leq 4000.

Input

The input is given from Standard Input in the following format:

w

Output

Print 2 lines.

In the first line, print the number of elements of a best representation of w.

In the second line, print the number of the best representations of w, modulo 1000000007.

Sample Input 1

aab

Sample Output 1

1
1

Sample Input 2

bcbc

Sample Output 2

2
3

In this case, there are 3 best representations of 2 elements:

(b,cbc)

(bc,bc)

(bcb,c)

Sample Input 3

ddd

Sample Output 3

3
1
Score : 200 points

Problem Statement

Snuke lives on an infinite two-dimensional plane. He is going on an N-day trip.
At the beginning of Day 1, he is at home. His plan is described in a string S of length N.
On Day i(1 ≦ i ≦ N), he will travel a positive distance in the following direction:

North if the i-th letter of S is N

West if the i-th letter of S is W

South if the i-th letter of S is S

East if the i-th letter of S is E

He has not decided each day's travel distance. Determine whether it is possible to set each day's travel distance so that he will be back at home at the end of Day N.

Constraints

1 ≦ | S | ≦ 1000

S consists of the letters N, W, S, E.

Input

The input is given from Standard Input in the following format:

S

Output

Print Yes if it is possible to set each day's travel distance so that he will be back at home at the end of Day N. Otherwise, print No.

Sample Input 1

SENW

Sample Output 1

Yes

If Snuke travels a distance of 1 on each day, he will be back at home at the end of day 4.

Sample Input 2

NSNNSNSN

Sample Output 2

Yes

Sample Input 3

NNEW

Sample Output 3

No

Sample Input 4

W

Sample Output 4

No
Score : 400 points

Problem Statement

Snuke has a large collection of cards. Each card has an integer between 1 and N, inclusive, written on it.
He has A_i cards with an integer i.

Two cards can form a pair if the absolute value of the difference of the integers written on them is at most 1.

Snuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create.

Constraints

1 ≦ N ≦ 10^5

0 ≦ A_i ≦ 10^9 (1 ≦ i ≦ N)

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum number of pairs that Snuke can create.

Sample Input 1

4
4
0
3
2

Sample Output 1

4

For example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4).

Sample Input 2

8
2
0
1
6
0
8
2
1

Sample Output 2

9
Score : 600 points

Problem Statement

Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct.
He is sorting this sequence in increasing order.
With supernatural power, he can perform the following two operations on the sequence in any order:

Operation 1: choose 2 consecutive elements, then reverse the order of those elements.

Operation 2: choose 3 consecutive elements, then reverse the order of those elements.

Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.

Constraints

1 ≦ N ≦ 10^5

0 ≦ A_i ≦ 10^9

If i ≠ j, then A_i ≠ A_j.

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of times Operation 1 that Snuke has to perform.

Sample Input 1

4
2
4
3
1

Sample Output 1

1

The given sequence can be sorted as follows:

First, reverse the order of the last three elements. The sequence is now: 2,1,3,4.

Then, reverse the order of the first two elements. The sequence is now: 1,2,3,4.

In this sequence of operations, Operation 1 is performed once. It is not possible to sort the sequence with less number of Operation 1, thus the answer is 1.

Sample Input 2

5
10
8
5
3
2

Sample Output 2

0
Score : 1100 points

Problem Statement

Snuke got positive integers s_1,...,s_N from his mother, as a birthday present. There may be duplicate elements.

He will circle some of these N integers. Since he dislikes cubic numbers, he wants to ensure that if both s_i and s_j (i ≠ j) are circled, the product s_is_j is not cubic. For example, when s_1=1,s_2=1,s_3=2,s_4=4, it is not possible to circle both s_1 and s_2 at the same time. It is not possible to circle both s_3 and s_4 at the same time, either.

Find the maximum number of integers that Snuke can circle.

Constraints

1 ≦ N ≦ 10^5

1 ≦ s_i ≦ 10^{10}

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
s_1
:
s_N

Output

Print the maximum number of integers that Snuke can circle.

Sample Input 1

8
1
2
3
4
5
6
7
8

Sample Output 1

6

Snuke can circle 1,2,3,5,6,7.

Sample Input 2

6
2
4
8
16
32
64

Sample Output 2

3

Sample Input 3

10
1
10
100
1000000007
10000000000
1000000009
999999999
999
999
999

Sample Output 3

9
Score : 1400 points

Problem Statement

Snuke got an integer sequence from his mother, as a birthday present. The sequence has N elements, and the i-th of them is i.
Snuke performs the following Q operations on this sequence. The i-th operation, described by a parameter q_i, is as follows:

Take the first q_i elements from the sequence obtained by concatenating infinitely many copy of the current sequence, then replace the current sequence with those q_i elements.

After these Q operations, find how many times each of the integers 1 through N appears in the final sequence.

Constraints

1 ≦ N ≦ 10^5

0 ≦ Q ≦ 10^5

1 ≦ q_i ≦ 10^{18}

All input values are integers.

Input

The input is given from Standard Input in the following format:

N Q
q_1
:
q_Q

Output

Print N lines. The i-th line (1 ≦ i ≦ N) should contain the number of times integer i appears in the final sequence after the Q operations.

Sample Input 1

5 3
6
4
11

Sample Output 1

3
3
3
2
0

After the first operation, the sequence becomes: 1,2,3,4,5,1.

After the second operation, the sequence becomes: 1,2,3,4.

After the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.

In this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.

Sample Input 2

10 10
9
13
18
8
10
10
9
19
22
27

Sample Output 2

7
4
4
3
3
2
2
2
0
0
Score : 1700 points

Problem Statement

Snuke got a grid from his mother, as a birthday present. The grid has H rows and W columns. Each cell is painted black or white. All black cells are 4-connected, that is, it is possible to traverse from any black cell to any other black cell by just visiting black cells, where it is only allowed to move horizontally or vertically.

The color of the cell at the i-th row and j-th column (1 ≦ i ≦ H, 1 ≦ j ≦ W) is represented by a character s_{ij}. If s_{ij} is #, the cell is painted black. If s_{ij} is ., the cell is painted white. At least one cell is painted black.

We will define fractals as follows.
The fractal of level 0 is a 1 × 1 grid with a black cell.
The fractal of level k+1 is obtained by arranging smaller grids in H rows and W columns, following the pattern of the Snuke's grid.
At a position that corresponds to a black cell in the Snuke's grid, a copy of the fractal of level k is placed.
At a position that corresponds to a white cell in the Snuke's grid, a grid whose cells are all white, with the same dimensions as the fractal of level k, is placed.

You are given the description of the Snuke's grid, and an integer K. Find the number of connected components of black cells in the fractal of level K, modulo 10^9+7.

Constraints

1 ≦ H,W ≦ 1000

0 ≦ K ≦ 10^{18}

Each s_{ij} is either # or ..

All black cells in the given grid are 4-connected.

There is at least one black cell in the given grid.

Input

The input is given from Standard Input in the following format:

H W K
s_{11} .. s_{1W}
:
s_{H1} .. s_{HW}

Output

Print the number of connected components of black cells in the fractal of level K, modulo 10^9+7.

Sample Input 1

3 3 3
.#.
###
#.#

Sample Output 1

20

The fractal of level K=3 in this case is shown below. There are 20 connected components of black cells.

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

Sample Input 2

3 3 3
###
#.#
###

Sample Output 2

1

Sample Input 3

11 15 1000000000000000000
.....#.........
....###........
....####.......
...######......
...#######.....
..##.###.##....
..##########...
.###.....####..
.####...######.
###############
#.##..##..##..#

Sample Output 3

301811921
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.
Score : 400 points

Problem Statement

Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.

You are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s.

Constraints

2 ≦ |s| ≦ 10^5

s consists of lowercase letters.

Partial Score

200 points will be awarded for passing the test set satisfying 2 ≦ N ≦ 100.

Input

The input is given from Standard Input in the following format:

s

Output

If there exists no unbalanced substring of s, print -1 -1.

If there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} ... s_{b} (1 ≦ a < b ≦ |s|), and print a b. If there exists more than one such substring, any of them will be accepted.

Sample Input 1

needed

Sample Output 1

2 5

The string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.

Sample Input 2

atcoder

Sample Output 2

-1 -1

The string atcoder contains no unbalanced substring.