The Tragedy of the Decreasing Growth Rate 1

Yurim felt that the growth rate of her height was slowing down, and she was very sad. One day she came across an expensive machine that measures height very precisely and bought it. The machine rounds the height to the nearest $\mathrm{cm}$ value with three decimal places, so its error margin is $0.5\times10^{-3}\mathrm{cm}$. When the height is $(m+0.5)\times10^{-3}\mathrm{cm}$ for an integer $m$, the machine rounds up to $(m+1)\times10^{-3}\mathrm{cm}$.

Yurim bought the machine the day before yesterday and measured her height at noon the day before that and at noon yesterday. Thanks to the precision, she could see that she was growing. She drew a table in her notebook and planned to record the daily growth there. Yesterday's height was $+0.006\mathrm{cm}$ higher than the day before, so she wrote 6, the last digit of the value, in yesterday's cell.

Today the daily growth was $+0.007\mathrm{cm}$, higher than yesterday. She wrote 7 in the next cell and told her classmates that her growth rate was not decreasing. The boast reached Dongwoo, the top student in school, who immediately spotted the flaw.

'Suppose her actual heights over three days were $140.0008\mathrm{cm}$, $140.0074\mathrm{cm}$, and $140.0138\mathrm{cm}$. Then the actual daily growth falls from $+0.0066\mathrm{cm}$ to $+0.0064\mathrm{cm}$. However, the machine rounds these to $140.001\mathrm{cm}$, $140.007\mathrm{cm}$, and $140.014\mathrm{cm}$, which match the daily growth you recorded. Can you still be sure that your growth rate is not decreasing?'

Dongwoo's point was that one set of recorded daily growth values can be explained by many different actual growths. Yurim had jumped to a conclusion without considering this.

That evening, Yurim could not sit still. Her friends had teased her about it on the way home. She feared the incident would become a permanent embarrassment and that she would soon be nicknamed the kid whose growth rate decreases.

Yurim decided to study how the recorded daily growth values relate to the actual growth that explains them. Then she would measure her height steadily for a while and produce new recorded data to refute Dongwoo. Help her plan the strategy.

Yurim recorded the daily growth for $N$ consecutive days. Her plan is to show that no actual growth can explain this data if the actual daily growth decreases monotonically. Here, monotonically decreasing means the values never go up, so a stretch of equal values still counts as decreasing.

Given the recorded daily growth data for $N$ consecutive days, determine whether such an actual growth is possible.

The first line contains an integer $N$ ($1 \leq N \leq 100\,000$). The second line contains the $N$ terms of the integer sequence, separated by spaces, in order. Each term is an integer from $0$ to $9$.

Interpret each term $a$ of the given sequence as $+(0.001\times a)\mathrm{cm}$ to form the recorded daily growth data. Print Provable if no actual growth with a monotonically decreasing daily growth can explain this data. Otherwise, print Not Provable, which means such an actual growth exists.