KSA has two dormitories, which are the boys' dormitory Gyeonwoo-gwan, and the girls' dormitory Jignyeo-gwan. Two cats, Nyannyan and Samsaek, live on a passage called Ojakgyo that lies between the two dormitories.
Jimin, who loves cats, wants to take a picture of Nyannyan and Samsaek when they are in their perfect positions. To do so, he tries to move the cats to his desired positions.
Assume Ojakgyo is a number line of integers $0,1,2,\cdots,N-1,N$. Gyeonwoo-gwan is located on point $0$, and Jignyeo-gwan is located on point $N$. Jimin and the cats can only stay on integer points.
Starting from $0$ seconds, the following steps are repeated.
- Jimin moves to any point on Ojakgyo he wants. This step takes $1$ second.
- The cats move according to the rules below. This step takes $0$ seconds.
Jimin cannot move to the point where Samsaek is located because he might get scratched.
Nyannyan and Samsaek move as follows.
- Nyannyan, who likes people, moves towards Jimin by $1$ every second. Nyannyan won't move if it is on the same point as Jimin.
- Samsaek, who is scared of people, moves away from Jimin by $1$ every second.
- Nyannyan and Samsaek can stay at the same point because they get along well.
Also, Jimin has to prevent Nyannyan and Samsaek from moving to Gyeonwoo-gwan($0$) or Jignyeo-gwan($N$) entrance. Jimin can move to either dormitory entrance.
Jimin can stop to take a picture if the cats are at the desired points after moving.
Given Ojakgyo's length $N$, Nyannyan and Samsaek's initial positions $A$ and $B$, and Nyannyan and Samsaek's desired positions $C$ and $D$, write a program that tells Jimin how he should move to take the desired picture.
Input
The first line contains an integer $N$.
The second line contains four space-separated integers $A$, $B$, $C$, and $D$.
Output
On the first line, print YES if there is a way to take the desired picture, and NO otherwise.
If such a way exists, let the time required to take the picture be $k$ seconds.
If $k>0$, print $k$ space-separated integers $x_1, x_2, \cdots, x_k$ on the second line. $x_i$ is the point Jimin will be on at the $i$-th second.
If $k=0$, do not print the second line.
$k$ must not exceed $3\times 10^5$. It can be proven that such a way exists when it is possible to take the picture.
If there are multiple solutions, print any of them. Note that you don't have to minimize $k$.
Constraints
- $2\leq N\leq 10^5$
- $0
Scoring
| No. | Points | Constraints | ||||
|---|---|---|---|---|---|---|
| 1 | 10 | $N\leq 100$ | ||||
| 2 | 10 | $N\leq 1000$ | ||||
| 3 | 20 | $ | A-B | \geq 2$; $ | C-D | \geq 2$ |
| 4 | 20 | $ | A-B | \geq 2$ | ||
| 5 | 40 | No additional constraints |
Examples
Input 1
3 1 2 1 2
Output 1
YES
Input 2
10 1 2 4 9
Output 2
YES 1 1 2 3 4 5 0
Input 3
10 1 1 5 6
Output 3
NO