MasterMind

MasterMind is a classic two-player game.

One player is the codemaker: she picks a four-digit secret number $S$ with $1000 \le S \le 9999$. The other player is the codebreaker, who repeatedly guesses four-digit numbers until she cracks the code.

For every codebreaker guess $G_i$ (with $1000 \le G_i \le 9999$), the codemaker replies with two integers:

• $C_i$ ($0 \le C_i \le 4$): how many digits of the guess are correct and in their correct position in the secret number.
• $W_i$ ($0 \le W_i \le 4 - C_i$): how many of the remaining digits (those not counted by $C_i$) are correct but in the wrong position.

For example, if the secret number is $2351$ and the codebreaker guesses $1350$, the feedback is 2 1: the digits $3$ and $5$ are in their correct positions, and $1$ is present but in the wrong position. As another example, in a five-digit variant, if the secret is $11223$ and the guess is $12322$, the feedback is 2 2.

You are given $N$ ($1 \le N \le 100$) guesses together with their feedback from the middle of a game. Output the smallest four-digit number (in the range $1000 \le S \le 9999$) that could still be the codemaker's secret, i.e. that is consistent with every guess and its feedback. If no such number exists, output NONE.

• Line 1: a single integer $N$.
• Lines 2 to $N+1$: line $i+1$ contains guess $i$ and its two responses as three space-separated integers $G_i$, $C_i$, and $W_i$.

• A single line with the smallest four-digit number (in the same range as the secret, $1000 \le S \le 9999$) that could be the secret code. If there is no such number, output a single line containing the word NONE.