Problem Statement

Takahashi melted and mixed A grams of gold and B grams of silver (0 \leq A,B,\ 0 \lt A+B) to produce new metal.

What metal did he produce: pure gold, pure silver, or an alloy?

Formally, the product is called as follows.

• Pure gold, if 0 \lt A and B=0.
• Pure silver, if A=0 and 0 \lt B.
• An alloy, if 0 \lt A and 0 \lt B.

Constraints

• 0 \leq A,B \leq 100
• 1 \leq A+B
• All values in input are integers.

Sample Input 1

50 50

Sample Output 1

Alloy

We have 0 \lt A and 0 \lt B, so the product is an alloy.

Sample Input 2

100 0

Sample Output 2

Gold

We have 0 \lt A and B=0, so the product is pure gold.

Sample Input 3

0 100

Sample Output 3

Silver

We have A=0 and 0 \lt B, so the product is pure silver.

Sample Input 4

100 2

Sample Output 4

Alloy

Problem Statement

There is a row of N people. They are described by a string S of length N. The i-th person from the front is male if the i-th character of S is M, and female if it is F.

Determine whether the men and women are alternating.

It is said that the men and women are alternating if and only if there is no position where two men or two women are adjacent.

Constraints

• 1 \leq N \leq 100
• N is an integer.
• S is a string of length N consisting of M and F.

Sample Input 1

6
MFMFMF

Sample Output 1

Yes

There is no position where two men or two women are adjacent, so the men and women are alternating.

Sample Input 2

9
FMFMMFMFM

Sample Output 2

No

Sample Input 3

1
F

Sample Output 3

Yes

Problem Statement

There are N people numbered Person 1, Person 2, \dots, and Person N. Person i has a family name s_i and a given name t_i.

Consider giving a nickname to each of the N people. Person i's nickname a_i should satisfy all the conditions below.

• a_i coincides with Person i's family name or given name. In other words, a_i = s_i and/or a_i = t_i holds.
• a_i does not coincide with the family name and the given name of any other person. In other words, for all integer j such that 1 \leq j \leq N and i \neq j, it holds that a_i \neq s_j and a_i \neq t_j.

Is it possible to give nicknames to all the N people? If it is possible, print Yes; otherwise, print No.

Constraints

• 2 \leq N \leq 100
• N is an integer.
• s_i and t_i are strings of lengths between 1 and 10 (inclusive) consisting of lowercase English alphabets.

Sample Input 1

3
tanaka taro
tanaka jiro
suzuki hanako

Sample Output 1

Yes

The following assignment satisfies the conditions of nicknames described in the Problem Statement: a_1 = taro, a_2 = jiro, a_3 = hanako. (a_3 may be suzuki, too.)
However, note that we cannot let a_1 = tanaka, which violates the second condition of nicknames, since Person 2's family name s_2 is tanaka too.

Sample Input 2

3
aaa bbb
xxx aaa
bbb yyy

Sample Output 2

No

There is no way to give nicknames satisfying the conditions in the Problem Statement.

Sample Input 3

2
tanaka taro
tanaka taro

Sample Output 3

No

There may be a pair of people with the same family name and the same given name.

Sample Input 4

3
takahashi chokudai
aoki kensho
snu ke

Sample Output 4

Yes

We can let a_1 = chokudai, a_2 = kensho, and a_3 = ke.

Problem Statement

You are given a positive integer N. If there are integers x and y such that N=2^x3^y, print Yes; otherwise, print No.

Constraints

• 1\leq N\leq10^{18}
• N is an integer.

Sample Input 1

324

Sample Output 1

Yes

For x=2,y=4, we have 2^x3^y=2^23^4=4\times81=324, so the condition is satisfied. Thus, you should print Yes.

Sample Input 2

5

Sample Output 2

No

There are no integers x and y such that 2^x3^y=5. Thus, you should print No.

Sample Input 3

32

Sample Output 3

Yes

For x=5,y=0, we have 2^x3^y=32\times1=32, so you should print Yes.

Sample Input 4

37748736

Sample Output 4

Yes

Problem Statement

You are given two sequences, each of length N, consisting of integers: A=(A_1, \ldots, A_N) and B=(B_1, \ldots, B_N).

Determine whether there is a sequence of length N, X=(X_1, \ldots, X_N), satisfying all of the conditions below.

• X_i = A_i or X_i = B_i, for every i(1\leq i\leq N).

• |X_i - X_{i+1}| \leq K, for every i(1\leq i\leq N-1).

Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq K \leq 10^9
• 1 \leq A_i,B_i \leq 10^9
• All values in input are integers.

Sample Input 1

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

Sample Output 1

Yes

X=(9,6,3,7,5) satisfies all conditions.

Sample Input 2

4 90
1 1 1 100
1 2 3 100

Sample Output 2

No

No X satisfies all conditions.

Sample Input 3

4 1000000000
1 1 1000000000 1000000000
1 1000000000 1 1000000000

Sample Output 3

Yes