{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eYou a given a permutation $p_1,p_2,\\dots,p_n$ of size $n$. Initially, all elements in $p$ are frozen. There will be $n$ stages that these elements will become available one by one. On stage $i$, the element $p_{k_i}$ will become available.\u003cbr\u003e\u003cbr\u003eFor each $i$, find the longest increasing subsequence among available elements after the first $i$ stages.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq 3)$, denoting the number of test cases.\u003cbr\u003e\u003cbr\u003eIn each test case, there is one integer $n(1\\leq n\\leq 50000)$ in the first line, denoting the size of permutation.\u003cbr\u003e\u003cbr\u003eIn the second line, there are $n$ distinct integers $p_1,p_2,...,p_n(1\\leq p_i\\leq n)$, denoting the permutation.\u003cbr\u003e\u003cbr\u003eIn the third line, there are $n$ distinct integers $k_1,k_2,...,k_n(1\\leq k_i\\leq n)$, describing each stage.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that $p_1,p_2,...,p_n$ and $k_1,k_2,...,k_n$ are generated randomly."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing $n$ integers, where the $i$-th integer denotes the length of the longest increasing subsequence among available elements after the first $i$ stages."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n5\r\n2 5 3 1 4\r\n1 4 5 3 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 1 2 3 3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}