404693: GYM101611 D Decoding of Varints

Varint is a type used to serializing integers using one or more bytes. The key idea is to have smaller values being encoded with a smaller number of bytes.

First, we would like to encode some unsigned integer x. Consider its binary representation x = a_0a1a2... a_k - 1, where a_i-th stands for the i-th significant bit, i.e. x = a₀·2⁰ + a₁·2¹ + ... + a_k - 1·2^k - 1, while k - 1 stands for the index of the most significant bit set to 1 or k = 1 if x = 0.

To encode x we will use bytes b₀, b₁, ..., b_m - 1. That means one byte for integers from 0 to 127, two bytes for integers from 128 to 2¹⁴ - 1 = 16383 and so on, up to ten bytes for 2⁶⁴ - 1. For bytes b₀, b₁, ..., b_m - 2 the most significant bit is set to 1, while for byte b_m - 1 it is set to 0. Then, for each i from 0 to k - 1, i mod 7 bit of byte is set to a_i. Thus,

In the formula above we subtract 128 from b₀, b₁, ..., b_m - 2 because their most significant bit was set to 1.

For example, integer 7 will be represented as a single byte b₀ = 7, while integer 260 is represented as two bytes b₀ = 132 and b₁ = 2.

To represent signed integers we introduce ZigZag encoding. As we want integers of small magnitude to have short representation we map signed integers to unsigned integers as follows. Integer 0 is mapped to 0,  - 1 to 1, 1 to 2,  - 2 to 3, 2 to 4,  - 3 to 5, 3 to 6 and so on, hence the name of the encoding. Formally, if x ≥ 0, it is mapped to 2x, while if x < 0, it is mapped to  - 2x - 1.

For example, integer 75 is mapped to 150 and is encoded as b₀ = 150, b₁ = 1, while  - 75 will be mapped to 149 and will be encoded as b₀ = 149, b₁ = 1. In this problem we only consider such encoding for integers from  - 2⁶³ to 2⁶³ - 1 inclusive.

You are given a sequence of bytes that corresponds to a sequence of signed integers encoded as varints. Your goal is to decode and print the original sequence.

The first line of the input contains one integer n (1 ≤ n ≤ 10 000) — the length of the encoded sequence. The next line contains n integers from 0 to 255. You may assume that the input is correct, i.e. there exists a sequence of integers from  - 2⁶³ to 2⁶³ - 1 that is encoded as a sequence of bytes given in the input.

Print the decoded sequence of integers.

5
0 194 31 195 31

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2017
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