AtCoder Regular Contest 104
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Problem Statement
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There are $N$ buildings under construction arranged in a row, numbered $1, 2, \ldots, N$ from left to right.
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Given is an integer sequence $X$ of length $N$. The height of Building $i$, $H_i$, can be one of the integers between $1$ and $X_i$ (inclusive).
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For each $i$ such that $1 \leq i \leq N$, let us define $P_i$ as follows:
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- If there is an integer
$j (1 \leq j < i)$such that$H_j > H_i$,$P_i$is the maximum such$j$. Otherwise,$P_i$is$-1$.
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Considering all possible combinations of the buildings' heights, find the number of integer sequences that $P$ can be, modulo $1000000007$.
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Constraints
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$1 \leq N \leq 100$$1 \leq X_i \leq 10^5$- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N
X_1 X_2 \cdots X_N翻译中…
Output
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Print the number of integer sequences that $P$ can be when all possible combinations of the buildings' heights are considered, modulo $1000000007$.
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样例
Input #1
3
3 2 1
Output #1
4
We have six candidates for $H$, as follows:
- $H = (1, 1, 1)$, for which $P$ is $(-1, -1, -1)$;
- $H = (1, 2, 1)$, for which $P$ is $(-1, -1, 2)$;
- $H = (2, 1, 1)$, for which $P$ is $(-1, 1, 1)$;
- $H = (2, 2, 1)$, for which $P$ is $(-1, -1, 2)$;
- $H = (3, 1, 1)$, for which $P$ is $(-1, 1, 1)$;
- $H = (3, 2, 1)$, for which $P$ is $(-1, 1, 2)$.
Thus, there are four integer sequences that $P$ can be: $(-1, -1, -1), (-1, -1, 2), (-1, 1, 1)$, and $(-1, 1, 2)$.
Input #2
3
1 1 2
Output #2
1
We have two candidates for $H$, as follows:
- $H = (1, 1, 1)$, for which $P$ is $(-1, -1, -1)$;
- $H = (1, 1, 2)$, for which $P$ is $(-1, -1, -1)$.
Thus, there is one integer sequence that $P$ can be.
Input #3
5
2 2 2 2 2
Output #3
16
Input #4
13
3 1 4 1 5 9 2 6 5 3 5 8 9
Output #4
31155
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。