{"raw_statement":[{"iden":"problem statement","content":"Snuke loves constructing integer sequences.\nThere are $N$ piles of stones, numbered $1$ through $N$. The pile numbered $i$ consists of $a_i$ stones.\nSnuke will construct an integer sequence $s$ of length $Σa_i$, as follows:\n\n1.  Among the piles with the largest number of stones remaining, let $x$ be the index of the pile with the smallest index. Append $x$ to the end of $s$.\n2.  Select a pile with one or more stones remaining, and remove a stone from that pile.\n3.  If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.\n\nWe are interested in the lexicographically smallest sequence that can be constructed. For each of the integers $1,2,3,...,N$, how many times does it occur in the lexicographically smallest sequence?"},{"iden":"constraints","content":"*   $1 ≤ N ≤ 10^{5}$\n*   $1 ≤ a_i ≤ 10^{9}$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_{N}$"},{"iden":"sample input 1","content":"2\n1 2"},{"iden":"sample output 1","content":"2\n1\n\nThe lexicographically smallest sequence is constructed as follows:\n\n*   Since the pile with the largest number of stones remaining is pile $2$, append $2$ to the end of $s$. Then, remove a stone from pile $2$.\n*   Since the piles with the largest number of stones remaining are pile $1$ and $2$, append $1$ to the end of $s$ (we take the smallest index). Then, remove a stone from pile $2$.\n*   Since the pile with the largest number of stones remaining is pile $1$, append $1$ to the end of $s$. Then, remove a stone from pile $1$.\n\nThe resulting sequence is $(2,1,1)$. In this sequence, $1$ occurs twice, and $2$ occurs once."},{"iden":"sample input 2","content":"10\n1 2 1 3 2 4 2 5 8 1"},{"iden":"sample output 2","content":"10\n7\n0\n4\n0\n3\n0\n2\n3\n0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}