Score : $300$ points

Problem Statement

Determine whether there is a string $S$ of length $N$ consisting of X and Y that satisfies the following condition.

Condition: Among the $(N - 1)$ pairs of consecutive characters in $S$,

• exactly $A$ are XX,
• exactly $B$ are XY,
• exactly $C$ are YX, and
• exactly $D$ are YY.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $A \geq 0$
• $B \geq 0$
• $C \geq 0$
• $D \geq 0$
• $A + B + C + D = N - 1$

Input

The input is given from Standard Input in the following format:

$N$ $A$ $B$ $C$ $D$

Output

If there is a string $S$ that satisfies the condition, print Yes; otherwise, print No.

5 1 1 1 1

Yes

For instance, if $S = {}$XXYYX, the pairs of consecutive characters are XX, XY, YY, and YX from left to right. Each pattern occurs exactly once, so the condition is satisfied.

5 1 2 1 0

Yes

For instance, $S = {}$XXYXY satisfies the condition.

5 0 4 0 0

No

No string satisfies the condition.