Problem Statement

The battery of Takahashi's smartphone has $N$ mAh capacity. At time $0.5$, $1.5$, $2.5$, and so on (that is, at time $n + 0.5$ for every integer $n$), the battery charge decreases by $1$ mAh. Takahashi will leave his house with his phone fully charged at time $0$, visit a cafe $M$ times, and return home at time $T$. He will stay at the $i$-th cafe from time $A_i$ to time $B_i$. During this stay, he charges his phone, so the battery charge does not decrease. Instead, at time $n + 0.5$ for every integer $n$, it increases by $1$. However, if it is already equal to the battery capacity, it does not increase nor decrease. Determine whether he can return home without the battery charge dropping to $0$ on the way.

Constraints

• $1 \le N \le 10^9$
• $1 \le M \le 1000$
• $1 \le T \le 10^9$
• $0 \lt A_1 \lt B_1 \lt A_2 \lt B_2 \lt A_3 \lt B_3 \lt \dots \lt A_M \lt B_M \lt T$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M T
A_1 B_1
A_2 B_2
A_3 B_3
\hspace{15pt} \vdots
A_M B_M

Output

If Takahashi can return home without the battery charge dropping to $0$ on the way, print Yes; otherwise, print No.