Route

A jogging route in the countryside is a loop, so the starting point is also the finishing point. Poles stand along the route at intervals of $1$ metre, and the height of the ground at each pole is measured in centimetres above sea level.

The poles are numbered $1$ to $N$ in the jogging direction. A jogger starts at pole $1$, passes poles $2, 3, \ldots, N$ in order, then comes back to pole $1$ and stops. The ground between two neighbouring poles is a straight line.

The $1$ metre section between two neighbouring poles is level, uphill, or downhill. It is level when the two heights are equal, uphill when the later pole is higher, downhill when the later pole is lower.

A plain, an up-slope, and a down-slope are the longest continuous stretches of level, uphill, and downhill sections in the jogging direction. The jogger stops at pole $1$, so a stretch never continues past the starting point. A stretch that ends at pole $1$ and a stretch that begins at pole $1$ are counted separately even when they are of the same kind.

Count the plains, the up-slopes, and the down-slopes on the route.

The first line contains the length of the route in metres, $N$. ($3 \le N \le 30000$)

Each of the next $N$ lines contains one pole height in the jogging direction. The $i$-th of these lines holds $H_i$, the height of pole $i$ in centimetres above sea level, a positive integer. ($1 \le H_i \le 30000$)

Print three numbers on one line in this order: the number of plains, the number of up-slopes, the number of down-slopes. Put one space between two adjacent numbers.