alexjercan/bugnet huggingface dataset:
Multi-Map

For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that

multiple elements can have equivalent keys

.

insert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.

get($key$): Print all values with the specified $key$.

delete($key$): Delete all elements with the specified $key$.

dump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.

Input

The input is given in the following format.

$q$
$query_1$
$query_2$
:
$query_q$

Each query $query_i$ is given by

0 $key$ $x$

or

1 $key$

or

2 $key$

or

3 $L$ $R$

where the first digits 0, 1, 2 and 3 represent insert, get, delete and dump operations.

Output

For each get operation, print the corresponding values in the order of insertions.

For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements in ascending order of the keys, in case of a tie, in the order of insertions.

Constraints

$1 \leq q \leq 200,000$

$1 \leq x \leq 1,000,000,000$

$1 \leq $ length of $key$ $ \leq 20$

$key$ consists of lower-case letters

$L \leq R$ in lexicographic order

The total number of elements printed by get operations does not exceed $500,000$

The total number of elements printed by dump operations does not exceed $500,000$

Sample Input 1

10
0 blue 6
0 red 1
0 blue 4
0 white 5
1 red
1 blue
2 red
1 black
1 red
3 w z

Sample Output 1

1
6
4
white 5
Set Union

Find the union of two sets $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$.

Input

The input is given in the following format.

$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$

Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.

Output

Print elements in the union in ascending order. Print an element in a line.

Constraints

$1 \leq n, m \leq 200,000$

$0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$

$0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$

Sample Input 1

3
1 5 8
2
5 9

Sample Output 1

1
5
8
9
Set Intersection

Find the intersection of two sets $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$.

Input

The input is given in the following format.

$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$

Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.

Output

Print elements in the intersection in ascending order. Print an element in a line.

Constraints

$1 \leq n, m \leq 200,000$

$0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$

$0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$

Sample Input 1

4
1 2 5 8
5
2 3 5 9 11

Sample Output 1

2
5
Set Difference

Find the difference of two sets $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$, $A - B$.

Input

The input is given in the following format.

$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$

Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.

Output

Print elements in the difference in ascending order. Print an element in a line.

Constraints

$1 \leq n, m \leq 200,000$

$0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$

$0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$

Sample Input 1

5
1 2 3 5 8
2
2 5

Sample Output 1

1
3
8
Set Symmetric Difference

Find the symmetric difference of two sets $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$.

Input

The input is given in the following format.

$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$

Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.

Output

Print elements in the symmetric difference in ascending order. Print an element in a line.

Constraints

$1 \leq n, m \leq 200,000$

$0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$

$0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$

Sample Input 1

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

Sample Output 1

1
3
5
7
8
Prime Factorization

Factorize a given integer n.

Input

n

An integer n is given in a line.

Output

Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.

Constraints

2 ≤ n ≤ 109

Sample Input 1

12

Sample Output 1

12: 2 2 3

Sample Input 2

126

Sample Output 2

126: 2 3 3 7
Power

For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Input

m n

Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Constraints

1 ≤ m ≤ 100

1 ≤ n ≤ 109

Sample Input 1

2 3

Sample Output 1

8

Sample Input 2

5 8

Sample Output 2

390625
Least Common Multiple

Find the least common multiple (LCM) of given n integers.

Input

n
a1 a2 ... an

n is given in the first line. Then, n integers are given in the second line.

Output

Print the least common multiple of the given integers in a line.

Constraints

2 ≤ n ≤ 10

1 ≤ ai ≤ 1000

Product of given integers ai(i = 1, 2, ... n) does not exceed 231-1

Sample Input 1

3
3 4 6

Sample Output 1

12

Sample Input 2

4
1 2 3 5

Sample Output 2

30
Euler's Phi Function

For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.

Input

n

An integer n (1 ≤ n ≤ 1000000000).

Output

The number of totatives in a line.

Sample Input 1

6

Sample Output 1

2

Sample Input 2

1000000

Sample Output 2

400000
Extended Euclid Algorithm

Given positive integers a and b, find the integer solution (x, y) to ax + by = gcd(a, b), where gcd(a, b) is the greatest common divisor of a and b.

Input

a b

Two positive integers a and b are given separated by a space in a line.

Output

Print two integers x and y separated by a space. If there are several pairs of such x and y, print that pair for which |x| + |y| is the minimal (primarily) and x ≤ y (secondarily).

Constraints

1 ≤ a, b ≤ 109

Sample Input 1

4 12

Sample Output 1

1 0

Sample Input 2

3 8

Sample Output 2

3 -1
Addition of Big Integers

Given two integers $A$ and $B$, compute the sum, $A + B$.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the sum in a line.

Constraints

$-1 \times 10^{100000} \leq A, B \leq 10^{100000}$

Sample Input 1

5 8

Sample Output 1

13

Sample Input 2

100 25

Sample Output 2

125

Sample Input 3

-1 1

Sample Output 3

0

Sample Input 4

12 -3

Sample Output 4

9
Difference of Big Integers

Given two integers $A$ and $B$, compute the difference, $A - B$.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the difference in a line.

Constraints

$-1 \times 10^{100000} \leq A, B \leq 10^{100000}$

Sample Input 1

5 8

Sample Output 1

-3

Sample Input 2

100 25

Sample Output 2

75

Sample Input 3

-1 -1

Sample Output 3

0

Sample Input 4

12 -3

Sample Output 4

15
Multiplication of Big Integers

Given two integers $A$ and $B$, compute the product, $A \times B$.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the product in a line.

Constraints

$-1 \times 10^{1000} \leq A, B \leq 10^{1000}$

Sample Input 1

5 8

Sample Output 1

40

Sample Input 2

100 25

Sample Output 2

2500

Sample Input 3

-1 0

Sample Output 3

0

Sample Input 4

12 -3

Sample Output 4

-36
Division of Big Integers

Given two integers $A$ and $B$, compute the quotient, $\frac{A}{B}$. Round down to the nearest decimal.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the quotient in a line.

Constraints

$-1 \times 10^{1000} \leq A, B \leq 10^{1000}$

$B \ne 0$

Sample Input 1

5 8

Sample Output 1

0

Sample Input 2

100 25

Sample Output 2

4

Sample Input 3

-1 3

Sample Output 3

0

Sample Input 4

12 -3

Sample Output 4

-4
Remainder of Big Integers

Given two integers $A$ and $B$, compute the remainder of $\frac{A}{B}$.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the remainder in a line.

Constraints

$0 \leq A, B \leq 10^{1000}$

$B \ne 0$

Sample Input 1

5 8

Sample Output 1

5

Sample Input 2

100 25

Sample Output 2

0
Multiplication of Big Integers II

Given two integers $A$ and $B$, compute the product, $A \times B$.

Input

Two integers $A$ and $B$ separated by a space character are given in a line.

Output

Print the product in a line.

Constraints

$-1 \times 10^{200000} \leq A, B \leq 10^{200000}$

Sample Input 1

5 8

Sample Output 1

40

Sample Input 2

100 25

Sample Output 2

2500

Sample Input 3

-1 0

Sample Output 3

0

Sample Input 4

12 -3

Sample Output 4

-36
Score : 100 points

Problem Statement

You are given an integer K.
Print the string obtained by repeating the string ACL K times and concatenating them.

For example, if K = 3, print ACLACLACL.

Constraints

1 \leq K \leq 5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the string obtained by repeating the string ACL K times and concatenating them.

Sample Input 1

3

Sample Output 1

ACLACLACL
Score : 200 points

Problem Statement

Snuke likes integers that are greater than or equal to A, and less than or equal to B.
Takahashi likes integers that are greater than or equal to C, and less than or equal to D.

Does there exist an integer liked by both people?

Constraints

0 \leq A \leq B \leq 10^{18}

0 \leq C \leq D \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print Yes or No.

Sample Input 1

10 30 20 40

Sample Output 1

Yes

For example, both like 25.

Sample Input 2

10 20 30 40

Sample Output 2

No
Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).
Score : 400 points

Problem Statement

You are given a sequence A_1, A_2, ..., A_N and an integer K.

Print the maximum possible length of a sequence B that satisfies the following conditions:

B is a (not necessarily continuous) subsequence of A.

For each pair of adjacents elements of B, the absolute difference of the elements is at most K.

Constraints

1 \leq N \leq 300,000

0 \leq A_i \leq 300,000

0 \leq K \leq 300,000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1
A_2
:
A_N

Output

Print the answer.

Sample Input 1

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

Sample Output 1

7

For example, B = (1, 4, 3, 6, 9, 7, 4) satisfies the conditions.

It is a subsequence of A = (1, 5, 4, 3, 8, 6, 9, 7, 2, 4).

All of the absolute differences between two adjacent elements (|1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4|) are at most K = 3.
Score : 500 points

Problem Statement

You have a string S of length N.
Initially, all characters in S are 1s.

You will perform queries Q times.
In the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit).
Then, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.

After each query, read the string S as a decimal integer, and print its value modulo 998,244,353.

Constraints

1 \leq N, Q \leq 200,000

1 \leq L_i \leq R_i \leq N

1 \leq D_i \leq 9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
L_1 R_1 D_1
:
L_Q R_Q D_Q

Output

Print Q lines.
In the i-th line print the value of S after the i-th query, modulo 998,244,353.

Sample Input 1

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

Sample Output 1

11222211
77772211
77333333
72333333
72311333

Sample Input 2

200000 1
123 456 7

Sample Output 2

641437905

Don't forget to take the modulo.
Score : 600 points

Problem Statement

There are 2N people numbered 1 through 2N.
The height of Person i is h_i.

How many ways are there to make N pairs of people such that the following conditions are satisfied?
Compute the answer modulo 998,244,353.

Each person is contained in exactly one pair.

For each pair, the heights of the two people in the pair are different.

Two ways are considered different if for some p and q, Person p and Person q are paired in one way and not in the other.

Constraints

1 \leq N \leq 50,000

1 \leq h_i \leq 100,000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
h_1
:
h_{2N}

Output

Print the answer.

Sample Input 1

2
1
1
2
3

Sample Output 1

2

There are two ways:

Form the pair (Person 1, Person 3) and the pair (Person 2, Person 4).

Form the pair (Person 1, Person 4) and the pair (Person 2, Person 3).

Sample Input 2

5
30
10
20
40
20
10
10
30
50
60

Sample Output 2

516
Score : 300 points

Problem Statement

There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).

For each k = 1,2,\dots,N, find the answer to the following question:

Rng is in City k.
Rng can perform the following move arbitrarily many times:

move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.

How many cities (including City k) are reachable from City k?

Constraints

1 \leq N \leq 200,000
(x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).
(y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).
All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print N lines. In i-th line print the answer to the question when k = i.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2

Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

7
6 4
4 3
3 5
7 1
2 7
5 2
1 6

Sample Output 2

3
3
1
1
2
3
2
Score : 600 points

Problem Statement

Given is an integer N.
Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N.
It can be proved that such a positive integer k always exists.

Constraints

1 \leq N \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer in a line.

Sample Input 1

11

Sample Output 1

10

1+2+\cdots+10=55 holds and 55 is indeed a multple of N=11.
There are no positive integers k \leq 9 that satisfy the condition, so the answer is k = 10.

Sample Input 2

20200920

Sample Output 2

1100144
Score : 600 points

Problem Statement

There is a board with N rows and M columns.
The information of this board is represented by N strings S_1,S_2,\ldots,S_N.
Specifically, the state of the square at the i-th row from the top and the j-th column from the left is represented as follows:

S_{i,j}=. : the square is empty.

S_{i,j}=# : an obstacle is placed on the square.

S_{i,j}=o : a piece is placed on the square.

Yosupo repeats the following operation:

Choose a piece and move it to its right adjecent square or its down adjacent square.
Moving a piece to squares with another piece or an obstacle is prohibited.
Moving a piece out of the board is also prohibited.

Yosupo wants to perform the operation as many times as possible.
Find the maximum possible number of operations.

Constraints

1 \leq N \leq 50

1 \leq M \leq 50

S_i is a string of length M consisting of ., # and o.

1 \leq ( the number of pieces )\leq 100.
In other words, the number of pairs (i, j) that satisfy S_{i,j}=o is between 1 and 100, both inclusive.

Input

Input is given from Standard Input in the following format:

N M
S_1
S_2
\vdots
S_N

Output

Print the maximum possible number of operations in a line.

Sample Input 1

3 3
o..
...
o.#

Sample Output 1

4

Yosupo can perform operations 4 times as follows:

o.. .o. ..o ... ...
... -> ... -> ... -> ..o -> ..o
o.# o.# o.# o.# .o#

Sample Input 2

9 10
.#....o#..
.#..#..##o
.....#o.##
.###.#o..o
#.#...##.#
..#..#.###
#o.....#..
....###..o
o.......o#

Sample Output 2

24
Score : 800 points

Problem Statement

There are N points on a number line, i-th of which is placed on coordinate X_i.
These points are numbered in the increasing order of coordinates.
In other words, for all i (1 \leq i \leq N-1), X_i < X_{i+1} holds.
In addition to that, an integer K is given.

Process Q queries.

In the i-th query, two integers L_i and R_i are given.
Here, a set s of points is said to be a good set if it satisfies all of the following conditions.
Note that the definition of good sets varies over queries.

Each point in s is one of X_{L_i},X_{L_i+1},\ldots,X_{R_i}.

For any two distinct points in s, the distance between them is greater than or equal to K.

The size of s is maximum among all sets that satisfy the aforementioned conditions.

For each query, find the size of the union of all good sets.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq K \leq 10^9

0 \leq X_1 < X_2 < \cdots < X_N \leq 10^9

1 \leq Q \leq 2 \times 10^5

1 \leq L_i \leq R_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
X_1 X_2 \cdots X_N
Q
L_1 R_1
L_2 R_2
\vdots
L_Q R_Q

Output

For each query, print the size of the union of all good sets in a line.

Sample Input 1

5 3
1 2 4 7 8
2
1 5
1 2

Sample Output 1

4
2

In the first query, you can have at most 3 points in a good set.
There exist two good sets: \{1,4,7\} and \{1,4,8\}.
Therefore, the size of the union of all good sets is |\{1,4,7,8\}|=4.

In the second query, you can have at most 1 point in a good set.
There exist two good sets: \{1\} and \{2\}.
Therefore, the size of the union of all good sets is |\{1,2\}|=2.

Sample Input 2

15 220492538
4452279 12864090 23146757 31318558 133073771 141315707 263239555 350278176 401243954 418305779 450172439 560311491 625900495 626194585 891960194
5
6 14
1 8
1 13
7 12
4 12

Sample Output 2

4
6
11
2
3
Score : 900 points

Problem Statement

Given are a permutation p_1, p_2, \dots, p_N of (1, 2, ..., N) and an integer K. Maroon performs the following operation for i = 1, 2, \dots, N - K + 1 in this order:

Shuffle p_i, p_{i + 1}, \dots, p_{i + K - 1} uniformly randomly.

Find the expected value of the inversion number of the sequence after all the operations are performed, and print it modulo 998244353.

More specifically, from the constraints of this problem, it can be proved that the expected value is always a rational number, which can be represented as an irreducible fraction \frac{P}{Q}, and that the integer R that satisfies R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353 is uniquely determined. Print this R.

Here, the inversion number of a sequence a_1, a_2, \dots, a_N is defined to be the number of ordered pairs (i, j) that satisfy i < j, a_i > a_j.

Constraints

2 \leq N \leq 200,000

2 \leq K \leq N

(p_1, p_2, \dots, p_N) is a permutation of (1, 2, \dots, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
p_1 p_2 ... p_N

Output

Print the expected value modulo 998244353.

Sample Input 1

3 2
1 2 3

Sample Output 1

1

The final sequence is one of (1, 2, 3), (2, 1, 3), (1, 3, 2), (2, 3, 1), each with probability \frac{1}{4}.
Their inversion numbers are 0, 1, 1, 2 respectively, so the expected value is 1.

Sample Input 2

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

Sample Output 2

164091855
Score : 1800 points

Problem Statement

Given are integer sequences A and B of length 3N. Each of these two sequences contains three copies of each of 1, 2, \dots, N.
In other words, A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).

Tak can perform the following operation to the sequence A arbitrarily many times:

Pick a value from 1, 2, \dots, N and call it x. A contains exactly three copies of x. Remove the middle element of these three. After that, append x to the beginning or the end of A.

Check if he can turn A into B. If he can, print the minimum required number of operations to achieve that.

Constraints

1 \leq N \leq 33

A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_{3N}
B_1 B_2 ... B_{3N}

Output

If Tak can turn A into B, print the minimum required number of operations to achieve that. Otherwise, print -1.

Sample Input 1

3
2 3 1 1 3 2 2 1 3
1 2 2 3 1 2 3 1 3

Sample Output 1

4

For example, Tak can perform operations as follows:

2 3 1 1 3 2 2 1 3 (The initial state)

2 2 3 1 1 3 2 1 3 (Pick x = 2 and append it to the beginning)

2 2 3 1 3 2 1 3 1 (Pick x = 1 and append it to the end)

1 2 2 3 1 3 2 3 1 (Pick x = 1 and append it to the beginning)

1 2 2 3 1 2 3 1 3 (Pick x = 3 and append it to the end)

Sample Input 2

3
1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3

Sample Output 2

0

Sample Input 3

3
2 3 3 1 1 1 2 2 3
3 2 2 1 1 1 3 3 2

Sample Output 3

-1

Sample Input 4

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

Sample Output 4

7
Score : 100 points

Problem Statement

In the Kingdom of AtCoder, people use a language called Taknese, which uses lowercase English letters.

In Taknese, the plural form of a noun is spelled based on the following rules:

If a noun's singular form does not end with s, append s to the end of the singular form.

If a noun's singular form ends with s, append es to the end of the singular form.

You are given the singular form S of a Taknese noun. Output its plural form.

Constraints

S is a string of length 1 between 1000, inclusive.

S contains only lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

Print the plural form of the given Taknese word.

Sample Input 1

apple

Sample Output 1

apples

apple ends with e, so its plural form is apples.

Sample Input 2

bus

Sample Output 2

buses

bus ends with s, so its plural form is buses.

Sample Input 3

box

Sample Output 3

boxs
Score : 200 points

Problem Statement

Tak performed the following action N times: rolling two dice.
The result of the i-th roll is D_{i,1} and D_{i,2}.

Check if doublets occurred at least three times in a row.
Specifically, check if there exists at lease one i such that D_{i,1}=D_{i,2}, D_{i+1,1}=D_{i+1,2} and D_{i+2,1}=D_{i+2,2} hold.

Constraints

3 \leq N \leq 100

1\leq D_{i,j} \leq 6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
D_{1,1} D_{1,2}
\vdots
D_{N,1} D_{N,2}

Output

Print Yes if doublets occurred at least three times in a row. Print No otherwise.

Sample Input 1

5
1 2
6 6
4 4
3 3
3 2

Sample Output 1

Yes

From the second roll to the fourth roll, three doublets occurred in a row.

Sample Input 2

5
1 1
2 2
3 4
5 5
6 6

Sample Output 2

No

Sample Input 3

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

Sample Output 3

Yes