Switching Lights

Farmer John keeps his cows sharp by letting them play with intellectual toys. One of the larger toys is the set of lights in the barn. Each of the N ($2 \le N \le 500$) cow stalls, conveniently numbered $1 \ldots N$, has a colorful light above it.

At the beginning of the evening, all lights are off. The cows control the lights with a set of N pushbutton switches. Pushing switch $i$ changes the state of light $i$ from off to on, or from on to off (a toggle).

The cows read and execute a list of M ($1 \le M \le 2000$) operations. Each operation is distinguished by a leading integer that is either $0$ or $1$.

An operation of type $0$ is followed by two integers $S$ and $E$ ($1 \le S \le E \le N$) indicating a starting and an ending switch. It is executed by pushing each switch from $S$ through $E$ inclusive exactly once.

An operation of type $1$ is followed by two integers $S$ and $E$ ($1 \le S \le E \le N$) specifying an inclusive range; the cows count how many lights are on within that range.

Process the entire list and produce the correct count for every type-$1$ operation.

• Line 1: Two space-separated integers, $N$ and $M$.
• Lines $2 \ldots M+1$: Each line describes one operation as three space-separated integers: the operation type, $S$, and $E$.

• For each type-$1$ (counting) operation, print the count as a single integer on its own line.

An example run with four lights and five commands:

          Lights
              1 2 3 4
  Init:       O O O O   O = off, * = on
  0 1 2  ->   * * O O   toggle lights 1 and 2
  0 2 4  ->   * O * *   toggle lights 2, 3, and 4
  1 2 3  ->   1         count lit lights in range 2..3
  0 2 4  ->   * * O O   toggle lights 2, 3, and 4
  1 1 4  ->   2         count lit lights in range 1..4