{"raw_statement":[{"iden":"statement","content":"For a string $s$ of length $n$, we define $p_j = x$ if $s[x\\ldots j]$ is the minimum suffix of $s[1\\ldots j]$, for all $j=1,\\ldots, n$. (A suffix is the minimum suffix of a string if it is lexicographically smaller than any other suffix of that string.)\n\nYou are to recover $s$ from $p_1,\\ldots, p_n$. If there are multiple answers, find the lexicographically smallest one."},{"iden":"input","content":"The first line contains a single integer $T$ ($1\\le T\\le 10^5$) representing the number of test cases.\n\nFor each test case, the first line contains a single integer $n$ ($1\\le n\\le 3\\times 10^6$) representing the length of $s$. The next line contains $n$ integers $p_1,\\ldots, p_n$ ($1\\le p_i\\le i$ for all $1\\le i\\le n$).\n\nIt is guaranteed that the sum of $n$ over all test cases does not exceed $3\\times 10^6$."},{"iden":"output","content":"For each test case, output one line. If there is no solution, output $-1$. Otherwise, output the lexicographically smallest $s$. Characters of $s$ are represented by positive integers. Smaller integers represent smaller characters in the lexicographical order."},{"iden":"note","content":"As the input/output can be huge, it is recommended to use fast input/output methods."}],"translated_statement":null,"sample_group":[["6\n3\n1 1 1\n3\n1 1 2\n3\n1 1 3\n3\n1 2 1\n3\n1 2 2\n3\n1 2 3","1 2 2\n-1\n1 2 1\n1 1 2\n2 1 2\n1 1 1"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}