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).

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.

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.

Sample Input 1

4 2
1 3 3 4
4 4 1 2

Sample Output 1

Yes

For example, X=(1,1,2,1) satisfies the condition.

Sample Input 2

3 2
1 2 2 3
2 2 1 1

Sample Output 2

No

No integer sequence X satisfies the condition.

Sample Input 3

15 20
2 5 6 14
11 14 10 10
13 15 6 10
8 10 3 8
7 8 1 9
2 8 14 15
14 14 5 12
6 10 9 9
1 4 10 14
5 14 6 7
8 10 5 8
8 10 11 15
4 8 4 11
7 9 1 4
8 10 3 3
11 13 8 14
6 13 4 15
4 7 6 11
2 5 1 2
8 14 6 8

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分