Networks

The company has $N$ network systems $S_1, S_2, \dots, S_N$ and $M$ networks $W_1, W_2, \dots, W_M$ that connect them. Each system has a priority, and every network carries data only from a higher-priority system to a lower-priority one. That is, if a network carries data from $S_A$ to $S_B$, then $A < B$.

The networks have become too tangled, so the company decided to tidy them up. For three systems $S_A$, $S_B$, and $S_C$, if there is a network from $S_A$ to $S_B$ and a network from $S_B$ to $S_C$, the two are merged into a single network from $S_A$ to $S_C$. The two original networks disappear and one new network appears. Several networks may connect the same pair of systems, and each of them counts as a separate network.

The company repeats this simplification to reduce the number of networks as much as possible. Find the number of networks that remain.

The first line contains $N$ and $M$. ($1 \le N, M \le 10^6$)

Each of the next $M$ lines contains two integers $A_i$ and $B_i$, meaning that $W_i$ carries data from $S_{A_i}$ to $S_{B_i}$. ($i = 1, 2, \dots, M$, $1 \le A_i < B_i \le N$)

Print the number of networks that remain after simplifying as much as possible.