Mian Guo is an ancient and vast country, and Fissure-Yang is its ruler, whom the citizens call the Mian Emperor. Mian Guo consists of $N$ cities, numbered $1$ to $N$. City $1$ is the most prestigious city in Mian Guo, so the Mian Emperor designated it as the capital, which we call the Mian Capital.

When the Mian Emperor first created the world, there were no roads. The only way to connect cities was through the Mian Emperor's prestige: for any $i \in [2, N]$, there was a one-way road from city $1$ to city $i$ with a length of $2^{60}$. Therefore, starting from the Mian Capital, it took $2^{60}$ units of time to reach any ordinary city.

However, after Mian Guo entered the industrial age, the citizens realized that relying on prestige for transportation was highly inefficient. Thus, the Mian Emperor began planning to build some one-way roads and entrusted this project to the Minister of Construction, Elephant.

Each road can be represented by a quadruple $(u, v, w, id)$, representing a one-way road from city $u$ to city $v$ with length $w$ and construction time $id$. Because Mian Guo's engineering capabilities are limited, the construction times of all roads are distinct.

After the roads are built, the Mian Emperor conducts an inspection. Because it is the Mian Emperor inspecting in person, the process is very meticulous and complex. You can refer to the provided spj.cpp to understand this process.

The Mian Emperor has a schedule $S$ recording several cities. The Mian Emperor inspects the cities in the order recorded in the schedule from beginning to end. Initially, the schedule only contains the Mian Capital, i.e., city $1$.

Furthermore, for each city $i$, the Mian Emperor records a value $dis_i$, representing the shortest path from city $1$ to city $i$ in the Mian Emperor's current impression. Initially, $dis_1 = 0$. Since the Mian Emperor can use prestige for transportation, for any city $i$ other than the Mian Capital, $dis_i = 2^{60}$ initially.

When the Mian Emperor inspects city $x$, he traverses all edges $(x, y, w)$ starting from $x$ in increasing order of their construction time and checks whether the shortest path to city $y$ can be updated. If it can be updated (i.e., $dis_y > dis_x + w$), the Mian Emperor sets $dis_y = w + dis_x$ and checks whether city $y$ will be inspected later according to the schedule. If it is not currently scheduled to be inspected later, he adds city $y$ to the end of the schedule.

(In another world, this inspection method is known as SPFA.)

However, the Mian Emperor's father, the "King of Ducks," once said: "As for SPFA, it is dead." Therefore, the Mian Emperor is very wary of SPFA, so he ordered Elephant to inspect on his behalf and submit the final schedule generated.

However, Elephant also had other things to do, so he just made up a schedule and submitted it. Now, the Mian Emperor would like to ask you to confirm whether there exists any road construction method such that the final schedule is identical to the one submitted by Elephant.

Input

The first line contains two positive integers $N$ and $K$, representing the number of cities and the length of the schedule submitted by Elephant, respectively.

The second line contains $K$ positive integers, giving the contents of the schedule in order from beginning to end.

Output

If there is no road construction method that makes the final schedule identical to the one given by Elephant, output the string "YouAreFake!" on the first line (without quotes, case-sensitive). Otherwise, output the string "YouAreWrite!" on the first line (without quotes, case-sensitive).

If a construction method exists, you need to output a solution in the following format:

On the second line, output an integer $M$, representing the number of roads. In the next $M$ lines, output the roads in increasing order of their construction time, with each line containing three integers $u, v, w$ representing a road from $u$ to $v$ with length $w$.

Your constructed solution must satisfy: $0 \leq M \leq K + 15$ and $0 \leq w \leq 2^{60}$.

Examples

Input 1

4 6
1 3 2 4 3 4

Output 1

YouAreWrite!
4
1 3 3
1 2 1
2 3 1
3 4 2

Subtasks

Task 1 (7 points): $1 \leq N \leq 3$.

Task 2 (8 points): It is guaranteed that all numbers in the schedule are distinct.

Task 3 (9 points): It is guaranteed that at most one number appears more than once in the schedule.

Task 4 (23 points): It is guaranteed that each number appears at most twice in the schedule.

Task 5 (53 points): No additional restrictions.

For all data, $1 \leq N \leq 100$, $1 \leq K \leq 10^4$, and each number in the schedule is an integer in $[1, N]$.