Revenge of BBuBBBlesort!

You are given a permutation of 1,2,...,N: p_1,p_2,...,p_N. Determine if the state where p_i=i for every i can be reached by performing the following operation any number of times:

• Choose three elements p_{i-1},p_{i},p_{i+1} (2\leq i\leq N-1) such that p_{i-1}>p_{i}>p_{i+1} and reverse the order of these three.

Constraints

• 3 \leq N \leq 3 × 10^5
• p_1,p_2,...,p_N is a permutation of 1,2,...,N.

Input

Input is given from Standard Input in the following format:

N p_1 : p_N

Output

If the state where p_i=i for every i can be reached by performing the operation, print Yes; otherwise, print No.

Examples

Input

5 5 2 1 4 3

Output

Yes

Input

4 3 2 4 1

Output

No

Input

7 3 2 1 6 5 4 7

Output

Yes

Input

6 5 3 4 1 2 6

Output

No

inputFormat

Input

Input is given from Standard Input in the following format:

N p_1 : p_N

outputFormat

Output

If the state where p_i=i for every i can be reached by performing the operation, print Yes; otherwise, print No.

Examples

Input

5 5 2 1 4 3

Output

Yes

Input

4 3 2 4 1

Output

No

Input

7 3 2 1 6 5 4 7

Output

Yes

Input

6 5 3 4 1 2 6

Output

No

样例

6
5
3
4
1
2
6

No