{"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\"\u003ePeter has a sequence $a_1,a_2,...,a_n$ and he define a function on the sequence -- $F(a_1,a_2,...,a_n)\u003d(f_1,f_2,...,f_n)$, where $f_i$ is the length of the longest increasing subsequence ending with $a_i$.\u003cbr\u003e\u003cbr\u003ePeter would like to find another sequence $b_1,b_2,...,b_n$ in such a manner that $F(a_1,a_2,...,a_n)$ equals to $F(b_1,b_2,...,b_n)$. Among all the possible sequences consisting of only positive integers, Peter wants the lexicographically smallest one.\u003cbr\u003e\u003cbr\u003eThe sequence $a_1, a_2, ..., a_n$ is lexicographically smaller than sequence $b_1, b_2, ..., b_n$, if there is such number $i$ from $1$ to $n$, that $a_k \u003d b_k$ for $1 \\le k \u0026lt; i$ and $a_i \u0026lt; b_i$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:\u003cbr\u003e\u003cbr\u003eThe first contains an integer $n$ $(1 \\le n \\le 100000)$ -- the length of the sequence. The second line contains $n$ integers $a_1,a_2,...,a_n$ $(1 \\le a_i \\le 10^9)$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output $n$ integers $b_1,b_2,...,b_n$ $(1 \\le b_i \\le 10^9)$ denoting the lexicographically smallest sequence.\u003cbr\u003e"}},{"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\u003e3\r\n1\r\n10\r\n5\r\n5 4 3 2 1\r\n3\r\n1 3 5\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n1 1 1 1 1\r\n1 2 3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}