Problem Statement

For an integer sequence $X=(X_1,X_2,\dots,X_n)$, let $X[L,R]$ denote the integer sequence $(X_L,X_{L+1},\dots,X_{R})$.

You are given integers $N$ and $M$, and $M$ quadruples of integers $(A_i,B_i,C_i,D_i)$.

Determine if there is an integer sequence $X$ of length $N$ that satisfies the following condition for every $i=1,2,\dots,M$:

• $X[A_i,B_i]$ is lexicographically smaller than $X[C_i,D_i]$.

What is lexicographical order on sequences? A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is lexicographically smaller than $T = (T_1,T_2,\ldots,T_{|T|})$ when 1. or 2. below holds. Here, $|S|$ and $|T|$ denotes the lengths of $S$ and $T$, respectively. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. There is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ that satisfy both of the following: $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$. $S_i$ is smaller than $T_i$ (as a number).

Constraints

• $2 \leq N \leq 2000$
• $1 \leq M \leq 2000$
• $1 \leq A_i \leq B_i \leq N$
• $1 \leq C_i \leq D_i \leq N$
• All input values are integers.

Input

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

N M
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
\vdots
A_M B_M C_M D_M

Output

If some integer sequence satisfies the condition, print Yes; otherwise, print No.