Problem:
Score : 1200 points

Problem Statement

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.

Sample Input 1

5
5
2
1
4
3

Sample Output 1

Yes

The state where p_i=i for every i can be reached as follows:

Reverse the order of p_1,p_2,p_3. The sequence p becomes 1,2,5,4,3.

Reverse the order of p_3,p_4,p_5. The sequence p becomes 1,2,3,4,5.

Sample Input 2

4
3
2
4
1

Sample Output 2

No

Sample Input 3

7
3
2
1
6
5
4
7

Sample Output 3

Yes

Sample Input 4

6
5
3
4
1
2
6

Sample Output 4

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
inline int read(){
	int  ans=0;
	char ch=getchar();
	while(!isdigit(ch))ch=getchar();
	while(isdigit(ch))ans=(ans<<3)+(ans<<1)+(ch^48),ch=getchar();
	return ans;
}
int a[300005],n;
inline bool check(int l,int r)
{
	int mn=n+1,mx=0;
	for(int i=l;i<=r;i++) mn=min(mn,a[i]),mx=max(mx,a[i]);
	if(mn!=l||mx!=r) return 0;
	int x=0,y=0;
	for(int i=l;i<=r;i+=2)
	{
		if(x<a[i]&&y<a[i]) y=a[i];
		else if(x<a[i]) x=a[i];
		else return 0;
	}
	return 1;
}
int main(){
	n=read();
	for(int i=1;i<=n;i++)
	{
		a[i]=read();
	}
	for(int i=1;i<=n;i++)
	{
		if((a[i]&1)!=(i&1)){cout<<"No";return 0;}
	}	
	for(int i=1;i<=n-2;i++)
	{
		if(a[i]==i) continue;
		int k=i;
		while(k<=n-2)
		{
			if(a[k+1]!=k+1) break;
			if(a[k+2]==k+2) break;
			k+=2;
		}
		if(!check(i,k)){cout<<"No";return 0;}
		i=k;
	}
	cout<<"Yes";
	return 0;
}