Many Easy Optimizations

AtCoder

IDarc187_d

Time5000ms

Memory256MB

Difficulty—

Define the **cost** of a sequence $X$ as (the maximum value of $X$ minus the minimum value of $X$). You are given sequences $A = (A_1, \ldots, A_N)$ and $B = (B_1, \ldots, B_N)$ of length $N$. Solve the following problem for $k = 1, 2, \ldots, N$. * Find the minimum possible cost of the sequence $C = (C_1, \ldots, C_k)$ whose $i$\-th element $C_i$ is $A_i$ or $B_i$. ## Constraints * All input numbers are integers. * $1 \leq N \leq 5 \times 10^5$ * $1 \leq A_i, B_i \leq 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ $B_1$ $\ldots$ $B_N$ [samples]

Samples

Input #1

3
8 11 10
7 6 1

Output #1

0
1
3

For $k=1$, if we choose $C = (8)$, the cost of $C$ is $0$, which is the minimum.
For $k=2$, if we choose $C = (7,6)$, the cost of $C$ is $1$, which is the minimum.
For $k=3$, if we choose $C = (8,11,10)$, the cost of $C$ is $3$, which is the minimum.

Input #2

10
43 35 36 58 25 7 61 4 96 3
55 29 88 15 99 49 67 57 92 49

Output #2

API Response (JSON)

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