{"problem":{"name":"A. Edit Distance","description":{"content":"A binary string is a non-empty sequence of $0$'s and $1$'s, e.g., _010110_, _1_, _11101_, etc. The edit distance of two binary strings $S$ and $T$, denoted by $e d i t (S, T)$, is the minimum number o","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10200A"},"statements":[{"statement_type":"Markdown","content":"A binary string is a non-empty sequence of $0$'s and $1$'s, e.g., _010110_, _1_, _11101_, etc. The edit distance of two binary strings $S$ and $T$, denoted by $e d i t (S, T)$, is the minimum number of single-character edit (insert, delete, or substitute) to modify $S$ into $T$. For example, the edit distance of _0011_ and _1100_ is $4$, i.e. _0011_ $arrow.r$ _011_ $arrow.r$ _11_ $arrow.r$ _110_ $arrow.r$ _1100_. The edit distance of _1100101_ and _1110100_ is $2$, i.e. _1100101_ $arrow.r$ _1110101_ $arrow.r$ _1110100_.\n\nAyu has a binary string $S$. She wants to find a binary string with the same length as $S$ that maximizes the edit distance with $S$. Formally, she wants to find a binary string $T_{m a x}$ such that $| S | = | T_{m a x} |$ and $e d i t (S, T_{m a x}) >= e d i t (S, T ')$ for all binary string $T '$ satisfying $| S | = | T ' |$.\n\nShe needs your help! However, since she wants to make your task easier, you are allowed to return any binary string $T$ with the same length as $S$ such that the edit distance of $S$ and $T$ is more than half the length of $S$. Formally, you must return a binary string $T$ such that $| S | = | T |$ and $e d i t (S, T) > frac(| S |, 2)$.\n\nOf course, you can still return $T_{m a x}$ if you want, since it can be proven that $e d i t (S, T_{m a x}) > frac(| S |, 2)$ for any binary string $S$. This also proves that there exists a solution for any binary string $S$. If there is more than one valid solution, you can output any of them.\n\nInput contains a binary string $S$ ($1 <= | S | <= 2000$).\n\nOutput in a line a binary string $T$ with the same length as $S$ that satisfies $e d i t (S, T) > frac(| S |, 2)$.\n\n_Explanation for the sample input/output #1_\n\nAs illustrated in the example above, the edit distance of _0011_ and _1100_ is $4$. Since $4 > frac(4, 2)$, _1100_ is one of the valid output for this sample.\n\n## Input\n\nInput contains a binary string $S$ ($1 <= | S | <= 2000$).\n\n## Output\n\nOutput in a line a binary string $T$ with the same length as $S$ that satisfies $e d i t (S, T) > frac(| S |, 2)$.\n\n[samples]\n\n## Note\n\n_Explanation for the sample input/output #1_As illustrated in the example above, the edit distance of _0011_ and _1100_ is $4$. Since $4 > frac(4, 2)$, _1100_ is one of the valid output for this sample.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nLet $ D_k = (d_{k,1}, d_{k,2}, \\dots, d_{k,12}) $ be a sequence of 12 distinct integers representing the estimated difficulties of problems A to L in the $ k $-th test case, where $ d_{k,i} $ is the difficulty of the $ i $-th problem.\n\n**Constraints**  \n1. $ 1 \\leq T \\leq 4096 $  \n2. For each $ k \\in \\{1, \\dots, T\\} $:  \n   - $ 1 \\leq d_{k,i} \\leq 100 $ for all $ i \\in \\{1, \\dots, 12\\} $  \n   - All $ d_{k,i} $ are distinct.\n\n**Objective**  \nFor each test case $ k $, determine whether the sequence $ D_k $ is in **strictly increasing order**.  \nThat is, output \"yes\" if $ d_{k,1} < d_{k,2} < \\dots < d_{k,12} $, otherwise output \"no\".","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10200A","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}