{"problem":{"name":"Inversions","description":{"content":"Snuke has an integer sequence $A$ whose length is $N$. He likes permutations of $(1, 2, ..., N)$, $P$, that satisfy the following condition: *   $P_i \\leq A_i$ for all $i$ ( $1 \\leq i \\leq N$ ). Snu","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc023_e"},"statements":[{"statement_type":"Markdown","content":"Snuke has an integer sequence $A$ whose length is $N$. He likes permutations of $(1, 2, ..., N)$, $P$, that satisfy the following condition:\n\n*   $P_i \\leq A_i$ for all $i$ ( $1 \\leq i \\leq N$ ).\n\nSnuke is interested in the inversion numbers of such permutations. Find the sum of the inversion numbers over all permutations that satisfy the condition. Since this can be extremely large, compute the sum modulo $10^9+7$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A_i \\leq N$ ( $1 \\leq i \\leq N$ )\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]\n\n## Notes\n\nThe _inversion number_ of a sequence $Z$ whose length $N$ is the number of pairs of integers $i$ and $j$ ( $1 \\leq i < j \\leq N$ ) such that $Z_i > Z_j$.","is_translate":false,"language":"English"}],"meta":{"iden":"agc023_e","tags":[],"sample_group":[["3\n2 3 3","4\n\nThere are four permutations that satisfy the condition: $(1,2,3)$, $(1,3,2)$, $(2,1,3)$ and $(2,3,1)$. The inversion numbers of these permutations are $0$, $1$, $1$ and $2$, respectively, for a total of $4$."],["6\n4 2 5 1 6 3","7\n\nOnly one permutation $(4,2,5,1,6,3)$ satisfies the condition. The inversion number of this permutation is $7$, so the answer is $7$."],["5\n4 4 4 4 4","0\n\nNo permutation satisfies the condition."],["30\n22 30 15 20 10 29 11 29 28 11 26 10 18 28 22 5 29 16 24 24 27 10 21 30 29 19 28 27 18 23","848414012"]],"created_at":"2026-03-03 11:01:14"}}