Vasya is a regular participant at programming contests and is already experienced in finding important sentences in long statements. Of course, numbers constraints are important — factorization of a number less than 1000000 is easier than of a number less than 1000000000. However, sometimes it's hard to understand the number at the first glance. Could it be shortened? For example, instead of 1000000 you could write $10^{6}$, instead of 1000000000  —$10^{9}$, instead of 1000000007 — $10^{9}+7$.

Vasya decided that, to be concise, the notation should follow several rules:

• the notation should only consist of numbers, operations of addition ("+"), multiplication ("*") and exponentiation ("^"), in particular, the use of braces is forbidden;
• the use of several exponentiation operations in a row is forbidden, for example, writing "2^3^4" is unacceptable;
• the value of the resulting expression equals to the initial number;
• the notation should consist of the minimal amount of symbols.

Given $n$, find the equivalent concise notation for it.