# Check if the game is valid or not

Three players P1, P2 and P3 are playing a game. But at a time only two players can play the game, so they decided, at a time two players will play the game and one will spectate. When one game ends, the one who lost the game becomes the spectator in the next game and the one who was spectating plays against the winner. There cannot be any draws in any game. Player P1 and P2 will play the first game. Input is the number of games played n and in next line winner of n games.

Examples:

```Input :
No. of Games : 4
Winner of the Game Gi : 1 1 2 3
Output : YES
Explanation :
Game1 : P1 vs P2 : P1 wins
Game2 : P1 vs P3 : P1 wins
Game3 : P1 vs P2 : P2 wins
Game4 : P3 vs P2 : P3 wins
None of the winners were invalid

Input :
No. of Games : 2
Winner of the Game Gi : 2 1
Output : NO
Explanation :
Game1 : P1 vs P2 : P2 wins
Game2 : P2 vs P3 : P1 wins (Invalid winner)
In Game2 P1 is spectator
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach :
Start with P1 and P2 and continue the game while making the loser new spectator by subtracting the current spectator and winner from total sum of three players i.e. 6. An invalid entry will halt the process.

Below is the implementation for the above approach:

## C++

```// CPP program to check if the game
// is valid
#include <bits/stdc++.h>
using namespace std;

string check_valid(int a[], int n)
{
// starting with player P1 and P2
// so making P3 spectator
int spec = 3;
for (int i = 0; i < n; i++) {

// If spectator wins a game
// then its not valid
if (a[i] == spec) {
return "Invalid";
}

// subtracting the current spectator
// and winner from total sum 6 which
// makes losing player spectator
spec = 6 - a[i] - spec;
}

// None of the winner is found spectator.
return "Valid";
}

// Driver program to test above functions
int main()
{
int n = 4;
int a[n] = {1, 1, 2, 3};
cout << check_valid(a, n);
return 0;
}

```

## Python3

```# Python3 code to check if the game
# is valid

def check_valid( a , n ):

# starting with player P1 and P2
# so making P3 spectator
spec = 3
for i in range(n):

# If spectator wins a game
# then its not valid
if a[i] == spec:
return "Invalid"

# subtracting the current spectator
# and winner from total sum 6 which
# makes losing player spectator
spec = 6 - a[i] - spec

# None of the winner is found spectator.
return "Valid"

# Driver code to test above functions
n = 4
a = [1, 1, 2, 3]
print(check_valid(a, n))

# This code is contributed by "Sharad_Bhardwaj".
```

Output:

```Valid
```

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