Problem Statement

A string consisting only of the digits $0$ and $1$ is called a bit string.

The input gives $2$ positive integers $N, M$ and a set $S$ with $M$ elements, consisting only of bit strings of length $N$.

$S$ is said to be a good set of bit strings if it satisfies all of the following $3$ conditions:

1. The string of length $N$ consisting only of the digit $1$ belongs to $S$.
2. For any elements $s_0, s_1$ of $S$, the bitwise AND of $s_0$ and $s_1$ belongs to $S$.
3. For any subset $S'$ of $S$, the bitwise OR of all elements of $S'$ belongs to $S$.

Here, in condition 3, the bitwise OR of all elements of $S'$ means the unique string $s$ of length $N$ consisting only of the digits $0$ and $1$ such that the following $2$ conditions hold for any positive integer $n$ not greater than $N$:

• If the $n$-th character from the right of $s$ is $1$, then there exists an element $s'$ of $S'$ whose $n$-th character from the right is $1$.
• If the $n$-th character from the right of $s$ is $0$, then there does not exist an element $s'$ of $S'$ whose $n$-th character from the right is $1$.

Determine whether $S$ is a good set of bit strings.

Background

Let $I_N$ be the set of all positive integers not greater than $N$, for each $s \in S$ let $U_s$ be the set of all $i \in I_N$ satisfying the condition "the $i$-th character from the right of $s$ is $1$", and let $\mathcal{O}_S$ be the family of sets $\{U_s \mid s \in S\}$. In this way, $S$ can be translated into the family $\mathcal{O}_S$ of subsets of $I_N$.

When geometry is formulated in modern set theory, the concept of a topological space is often used. The pair $(I_N,\mathcal{O}_S)$ is a topological space if and only if it satisfies all of the following $3$ conditions:

1. $I_N$ belongs to $\mathcal{O}_S$.
2. For any elements $U_0, U_1$ of $\mathcal{O}_S$, $U_0 \cap U_1$ belongs to $\mathcal{O}_S$.
3. For any subset $\mathcal{U}$ of $\mathcal{O}_S$, $\bigcup_{U \in \mathcal{U}} U$ belongs to $\mathcal{O}_S$.

Therefore, by definition, this condition is equivalent to $S$ being a good set of bit strings. In other words, this problem is equivalent to determining whether $(I_N,\mathcal{O}_S)$ is a topological space.

Input

Number the elements of $S$ by the positive integers $m$ not greater than $M$, and denote them by $s_m$.

Then, the input is given from Standard Input in $1 + M$ lines in the following format:

• On line $1$, $N, M$ are given, separated by a half-width space.
• For each positive integer $m$ not greater than $M$, $s_m$ is given on line $1 + m$.

$N$ $M$
$s_1$
$\vdots$
$s_M$

Constraints

The input satisfies the following constraints:

• $N$ is an integer satisfying $1 \leq N \leq 16$
• $M$ is an integer satisfying $1 \leq M \leq \min \{2^N,2^{12}\}$
• For any positive integer $m$ not greater than $M$, $s_m$ is a string of length $N$ consisting only of the digits $0$ and $1$

Output

Print Yes if $S$ is a good set of bit strings, and No otherwise.

Print a newline at the end.

Sample

1 1
0

No

1 1
1

No

1 2
0
1

Yes

3 4
000
011
110
111

No