To solve this problem, you need to keep track of the number on the board as it is updated by multiplying it with each element from the sequence `a`

, and after each step, we must check if the resulting number is a perfect square.

Pseudocode:

- Read the input.
- Start with the number
`1`

on the board. - For each element in the sequence, multiply it with the current number on the board and check if the result is a perfect square.
- Output "yes" or "no" based on whether the current product is a perfect square.

```
using System;
class PerfectSquareChecker
{
// Helper function to check if a number is a perfect square
static bool IsPerfectSquare(long x)
{
if (x < 0) return false;
long sqrtX = (long)Math.Sqrt(x);
return sqrtX * sqrtX == x;
}
static void Main()
{
// Read the input
int n = int.Parse(Console.ReadLine()); // Number of elements in the sequence
string[] input = Console.ReadLine().Split(); // Sequence of numbers as strings
long[] a = new long[n];
for (int i = 0; i < n; i++)
{
a[i] = long.Parse(input[i]); // Parse each element into a long array
}
// Start with 1 on the board
long currentNumber = 1;
// Process each number in the sequence
for (int i = 0; i < n; i++)
{
currentNumber *= a[i]; // Multiply current number with a[i]
// Check if the current number is a perfect square
if (IsPerfectSquare(currentNumber))
{
Console.WriteLine("yes");
}
else
{
Console.WriteLine("no");
}
}
}
}
```

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hth

Marcin