The ten Chinese characters of "New Hope Cup National Mathematics Contest" respectively represent 10 different natural numbers, and satisfy the conditions: new = hope + hope, hope = cup + whole, hope = whole + country, cup = number + learning, country = Big + game. If "number" is 4, what is the minimum value of "new".
"新希望杯全国数学大赛"这十个汉字分别表示10个不同的自然数，且满足条件：新=希+望，希=杯+全，望=全+国，杯=数+学，国=大+赛．若"数"为4，则"新"最小是多少．
<gadget id="calculator">3 + 5</gadget>
<output>8</output>

<gadget id="calculator">3 + 9</gadget>
<output>12</output>

<gadget id="calculator">8 + 12</gadget>
<output>20</output>

<result>20</result>