B - Two Arrays

Time Limit: 2 sec / Memory Limit: 256 MB

• a_i2 を足す
• b_j1 を足す

### 制約

• 1 ≤ N ≤ 10,000
• 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
• 入力は全て整数

### 入力

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N


### 入力例 1

3
1 2 3
5 2 2


### 出力例 1

Yes


• 1 回目： i=1,j=2. これによって a = \{3,2,3\}, b = \{5,3,2\} となります。
• 2 回目： i=1,j=2. これによって a = \{5,2,3\}, b = \{5,4,2\} となります。
• 3 回目： i=2,j=3. これによって a = \{5,4,3\}, b = \{5,4,3\} となります。

### 入力例 2

5
3 1 4 1 5
2 7 1 8 2


### 出力例 2

No


### 入力例 3

5
2 7 1 8 2
3 1 4 1 5


### 出力例 3

No


Score : 300 points

### Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

### Constraints

• 1 ≤ N ≤ 10 000
• 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
• All input values are integers.

### Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N


### Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

### Sample Input 1

3
1 2 3
5 2 2


### Sample Output 1

Yes


For example, we can perform three operations as follows to do our job:

• First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.
• Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.
• Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

### Sample Input 2

5
3 1 4 1 5
2 7 1 8 2


### Sample Output 2

No


### Sample Input 3

5
2 7 1 8 2
3 1 4 1 5


### Sample Output 3

No