You are given a simple undirected graph with $N$ vertices and $M$ edges. The $i$-th edge connects vertices $u_i$ and $v_i$ bidirectionally.

Determine if there exists a way to write an integer between $1$ and $2^{60} - 1$, inclusive, on each vertex of this graph so that the following condition is satisfied:

• For every vertex $v$ with a degree of at least $1$, the total XOR of the numbers written on its adjacent vertices (excluding $v$ itself) is $0$.

What is XOR?<

The XOR of two non-negative integers $A$ and $B$, denoted as $A \oplus B$, is defined as follows:

• In the binary representation of $A \oplus B$, the bit at position $2^k \, (k \geq 0)$ is $1$ if and only if exactly one of the bits at position $2^k$ in the binary representations of $A$ and $B$ is $1$. Otherwise, it is $0$.

For example, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$).
In general, the bitwise XOR of $k$ integers $p_1, \dots, p_k$ is defined as $(\cdots ((p_1 \oplus p_2) \oplus p_3) \oplus \cdots \oplus p_k)$. It can be proved that this is independent of the order of $p_1, \dots, p_k$.

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

```
$N$ $M$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_M$ $v_M$
```

If there is no way to write integers satisfying the condition, print No.

Otherwise, let $X_v$ be the integer written on vertex $v$, and print your solution in the following format. If multiple solutions exist, any of them will be accepted.

Yes

$X_1$ $X_2$ $\dots$ $X_N$

-   $1 \leq N \leq 60$
-   $0 \leq M \leq N(N-1)/2$
-   $1 \leq u_i &lt; v_i \leq N$
-   $(u_i, v_i) \neq (u_j, v_j)$ for $i \neq j$.
-   All input values are integers.

Yes
4 4 4

Other acceptable solutions include writing $(2,2,2)$ or $(3,3,3)$.

Yes
1

Any integer between $1$ and $2^{60} - 1$ can be written.