{"raw_statement":[{"iden":"problem statement","content":"Takahashi has $N$ balls. Each ball has an integer not less than $2$ written on it. He will insert them in a cylinder one by one. The integer written on the $i$\\-th ball is $a_i$.\nThe balls are made of special material. When $k$ balls with $k$ $(k \\geq 2)$ written on them line up in a row, all these $k$ balls will disappear.\nFor each $i$ $(1 \\leq i \\leq N)$, find the number of balls after inserting the $i$\\-th ball."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $2 \\leq a_i \\leq 2 \\times 10^5 \\, (1 \\leq i \\leq N)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $\\ldots$ $a_N$"},{"iden":"sample input 1","content":"5\n3 2 3 2 2"},{"iden":"sample output 1","content":"1\n2\n3\n4\n3\n\nThe content of the cylinder changes as follows.\n\n*   After inserting the $1$\\-st ball, the cylinder contains the ball with $3$.\n*   After inserting the $2$\\-nd ball, the cylinder contains $3, 2$ from bottom to top.\n*   After inserting the $3$\\-rd ball, the cylinder contains $3, 2, 3$ from bottom to top.\n*   After inserting the $4$\\-th ball, the cylinder contains $3, 2, 3, 2$ from bottom to top.\n*   After inserting the $5$\\-th ball, the cylinder momentarily has $3, 2, 3, 2, 2$ from bottom to top. The two consecutive balls with $2$ disappear, and the cylinder eventually contains $3, 2, 3$ from bottom to top.\n\n![image](https://img.atcoder.jp/ghi/ABC240D_sample.png)"},{"iden":"sample input 2","content":"10\n2 3 2 3 3 3 2 3 3 2"},{"iden":"sample output 2","content":"1\n2\n3\n4\n5\n3\n2\n3\n1\n0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}