String Fair

AtCoder

IDabc264_g

Time2000ms

Memory256MB

Difficulty—

In a string fair, they determine the _beauty_ of a non-empty string $S$ consisting of lowercase English letters. The beauty of string $S$ equals the sum of $N$ scores determined by $N$ criteria. For $i = 1, 2, \ldots, N$, the score determined by the $i$\-th criterion is "the number of occurrences of a string $T_i$ (of length **at most $3$** given in the Input) in $S$ as a consecutive subsequence" multiplied by $P_i$. Print the maximum possible beauty of a **non-empty** string $S$ consisting of lowercase English letters. If it is possible to obtain infinitely large beauty, print `Infinity` instead. Here, the number of occurrences of a string $V$ in a string $U = U_1U_2\ldots U_{|U|}$ as a consecutive subsequence is defined to be the number of integers $i$ such that $1 \leq i \leq |U|-|V|+1$ and $U_iU_{i+1}\ldots U_{i+|V|-1} = V$. ## Constraints * $1 \leq N \leq 18278$ * $N$ is an integer. * $T_i$ is a string of length between $1$ and $3$ consisting of lowercase English letters. * $i \neq j \Rightarrow T_i \neq T_j$ * $-10^9 \leq P_i \leq 10^9$ * $P_i$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ $T_1$ $P_1$ $T_2$ $P_2$ $\vdots$ $T_N$ $P_N$ [samples]

Samples

Input #1

3
a -5
ab 10
ba -20

Output #1

Infinity

For example, if $S =$ `abzabz`:

*   The score determined by the $1$\-st criterion is $2 \times (-5) = -10$ points, because `a` occurs twice in $S$ as a consecutive subsequence.
*   The score determined by the $2$\-nd criterion is $2 \times 10 = 20$ points, because `ab` occurs twice in $S$ as a consecutive subsequence.
*   The score determined by the $3$\-rd criterion is $0 \times (-20) = 0$ points, because `ba` occurs $0$ times in $S$ as a consecutive subsequence.

Thus, the beauty of $S$ is $(-10) + 20 + 0 = 10$.
As another example, if $S =$ `abzabzabz`:

*   The score determined by the $1$\-st criterion is $3 \times (-5) = -15$ points, because `a` occurs $3$ times in $S$ as a consecutive subsequence.
*   The score determined by the $2$\-nd criterion is $3 \times 10 = 30$ points, because `ab` occurs $3$ times in $S$ as a consecutive subsequence.
*   The score determined by the $3$\-rd criterion is $0 \times (-20) = 0$ points, because `ba` occurs $0$ times in $S$ as a consecutive subsequence.

Thus, the beauty of $S$ is $(-15) + 30 + 0 = 15$.
In general, for a positive integer $X$, if $S$ is a concatenation of $X$ copies of `abz`, then the beauty of $S$ is $5X$. Since you can obtain as large beauty as you want, `Infinity` should be printed.

Input #2

28
a -5
ab 10
ba -20
bb -20
bc -20
bd -20
be -20
bf -20
bg -20
bh -20
bi -20
bj -20
bk -20
bl -20
bm -20
bn -20
bo -20
bp -20
bq -20
br -20
bs -20
bt -20
bu -20
bv -20
bw -20
bx -20
by -20
bz -20

Output #2

5

$S = $ `ab` achieves the maximum beauty possible.

Input #3

26
a -1
b -1
c -1
d -1
e -1
f -1
g -1
h -1
i -1
j -1
k -1
l -1
m -1
n -1
o -1
p -1
q -1
r -1
s -1
t -1
u -1
v -1
w -1
x -1
y -1
z -1

Output #3

\-1

Note that $S$ should be a non-empty string.

API Response (JSON)

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    "name": "String Fair",
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      "content": "In a string fair, they determine the _beauty_ of a non-empty string $S$ consisting of lowercase English letters. The beauty of string $S$ equals the sum of $N$ scores determined by $N$ criteria. For $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc264_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In a string fair, they determine the _beauty_ of a non-empty string $S$ consisting of lowercase English letters.\nThe beauty of string $S$ equals the sum of $N$ scores determined by $N$ criteria. For $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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