{"problem":{"name":"Prime Flip","description":{"content":"There are infinitely many cards, numbered $1$, $2$, $3$, $...$ Initially, Cards $x_1$, $x_2$, $...$, $x_N$ are face up, and the others are face down. Snuke can perform the following operation repeated","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc080_d"},"statements":[{"statement_type":"Markdown","content":"There are infinitely many cards, numbered $1$, $2$, $3$, $...$ Initially, Cards $x_1$, $x_2$, $...$, $x_N$ are face up, and the others are face down.\nSnuke can perform the following operation repeatedly:\n\n*   Select a prime $p$ greater than or equal to $3$. Then, select $p$ consecutive cards and flip all of them.\n\nSnuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.\n\n## Constraints\n\n*   $1 ≤ N ≤ 100$\n*   $1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$x_1$ $x_2$ $...$ $x_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc080_d","tags":[],"sample_group":[["2\n4 5","2\n\nBelow is one way to achieve the objective in two operations:\n\n*   Select $p = 5$ and flip Cards $1$, $2$, $3$, $4$ and $5$.\n*   Select $p = 3$ and flip Cards $1$, $2$ and $3$."],["9\n1 2 3 4 5 6 7 8 9","3\n\nBelow is one way to achieve the objective in three operations:\n\n*   Select $p = 3$ and flip Cards $1$, $2$ and $3$.\n*   Select $p = 3$ and flip Cards $4$, $5$ and $6$.\n*   Select $p = 3$ and flip Cards $7$, $8$ and $9$."],["2\n1 10000000","4"]],"created_at":"2026-03-03 11:01:13"}}