{"problem":{"name":"Good Sequence","description":{"content":"You are given a sequence of positive integers of length $N$, $a = (a_1, a_2, ..., a_N)$. Your objective is to remove some of the elements in $a$ so that $a$ will be a **good sequence**. Here, an seque","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc087_a"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence of positive integers of length $N$, $a = (a_1, a_2, ..., a_N)$. Your objective is to remove some of the elements in $a$ so that $a$ will be a **good sequence**.\nHere, an sequence $b$ is a **good sequence** when the following condition holds true:\n\n*   For each element $x$ in $b$, the value $x$ occurs exactly $x$ times in $b$.\n\nFor example, $(3, 3, 3)$, $(4, 2, 4, 1, 4, 2, 4)$ and $()$ (an empty sequence) are good sequences, while $(3, 3, 3, 3)$ and $(2, 4, 1, 4, 2)$ are not.\nFind the minimum number of elements that needs to be removed so that $a$ will be a good sequence.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $a_i$ is an integer.\n*   $1 \\leq a_i \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc087_a","tags":[],"sample_group":[["4\n3 3 3 3","1\n\nWe can, for example, remove one occurrence of $3$. Then, $(3, 3, 3)$ is a good sequence."],["5\n2 4 1 4 2","2\n\nWe can, for example, remove two occurrences of $4$. Then, $(2, 1, 2)$ is a good sequence."],["6\n1 2 2 3 3 3","0"],["1\n1000000000","1\n\nRemove one occurrence of $10^9$. Then, $()$ is a good sequence."],["8\n2 7 1 8 2 8 1 8","5"]],"created_at":"2026-03-03 11:01:13"}}