Problem Statement

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 $p_1, \dots, p_k$.

Constraints

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

Input

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

Output

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