The unit prices of both red and blue pens are integers, and the red pen is more expensive than the blue pen. Xiao Ming bought a red pen and a blue pen, and the total cost was 23 yuan. Xiaoqiang intends to use 109 yuan to buy these two kinds of pens (it is also allowed to buy only one of them), but no matter how he buys, he cannot use up 109 yuan exactly. Find the unit price of the red pen.
红、蓝两种笔的单价都是整数元，并且红笔比蓝笔贵．小明买红笔、蓝笔各一支，共用了23元．小强打算用109元来买这两种笔(也允许只买其中一种)，可是他无论怎么买，都不能把109元恰好用完．求红笔的单价．
<result>12</result>