Binary formats often use compact representations for integers. Consider writing a 32-bit unsigned integer to a file: you must always reserve 4 bytes to represent it (remember, 8 bits make one byte). However, in many real-life applications, integer values tend to be small. Writing these small values using a fixed 4-byte representation results in files that are mostly filled with zero bytes.
To make the representation more compact, we introduce the following encoding scheme. Each value is represented as a sequence of bytes , where each is an integer between and , inclusive. The most significant bit of each byte serves as a continuation flag, and the lower bits carry the actual data. If the continuation flag is , more bytes follow; for the last byte, it is . The representation is , meaning that contains the most significant bits of the encoded value.
For example, here's how to find the compact representation of . First, we find its binary representation:
Next, we split it into 7-bit chunks, padding with zeros on the left if necessary:
:::align{center}
/ /
:::
The first two chunks have a following chunk, so the corresponding bytes have their most significant bit set to . The last chunk has no following chunk, so its most significant bit is . This gives us:
You are given an integer , and your task is to find its compact representation.
输入格式
The only line contains a single integer ().
输出格式
Print a sequence of integers between and , inclusive, representing the compact encoding of . The encoding must not contain leading bytes with zero data bits: that is, it may not start with .
