Polycarp has a string $s[1 \dots n]$ of length $n$ consisting of decimal digits. Polycarp performs the following operation with the string $s$ no more than once (i.e. he can perform operation $0$ or $1$ time):

• Polycarp selects two numbers $i$ and $j$ ($1 \leq i \leq j \leq n$) and removes characters from the $s$ string at the positions $i, i+1, i+2, \ldots, j$ (i.e. removes substring $s[i \dots j]$). More formally, Polycarp turns the string $s$ into the string $s_1 s_2 \ldots s_{i-1} s_{j+1} s_{j+2} \ldots s_{n}$.

For example, the string $s =$"20192020" Polycarp can turn into strings:

• "2020" (in this case $(i, j)=(3, 6)$ or $(i, j)=(1, 4)$);
• "2019220" (in this case $(i, j)=(6, 6)$);
• "020" (in this case $(i, j)=(1, 5)$);
• other operations are also possible, only a few of them are listed above.

Polycarp likes the string "2020" very much, so he is wondering if it is possible to turn the string $s$ into a string "2020" in no more than one operation? Note that you can perform zero operations.