灵里的 lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm lukewarm. \end{array}\right.$ Step 2: Check if the first 20 terms. \end{enumerate} $1024=2^{10}=1024$ $2^{10}=1024$ $2^{11}=2048$ $2^{12}=4096$ $2^{13}=8192$ $2^{14}=16384$ $2^{15}=32768$ $2^{16}=65536$ $2^{17}=131072$ $2^{18}=262144$ $2^{19}=524288$ $2^{20}=1048576$ $2^{21}=2097152$ $2^{22}=4194304$ $2^{23}=8388608$ $2^{24}=16777216$ $2^{25}=33554432$ $2^{26}=67108864$ $2^{27}=134217728$ $2^{28}=268435456$ $2^{29}=536870912$ $2^{30}=1073741824$ $2^{31}=2147483648$ $2^{32}=4294967296$ $2^{33}=8589934592$ $2^{34}=17179869184$ $2^{35}=34359738368$ $2^{36}=68719476736$ $2^{37}=137438953472$ $2^{38}=274877906944$ $2^{39}=549755813888$ $2^{40}=1099511627776$ Thus we see that the largest power of $2$ less than $10^{10}$ is $2^{33}$. [Answer 14] $1024=2^{10}$ So $2^{10}$ divides $n$. Since $n$ is a perfect square, the exponents of all primes in its prime factorization must be even. So $n$ must be divisible by an even power of 2, at least $2^{10}$. $n \ge 2^{10}$ $n \ge 1024$ The smallest such $n$ is $2^{10}=1024$ itself which is a perfect square of $2^5=32$. $32^2=1024$ Thus, $1024=2^{10}$ is the smallest perfect square which is also a power of 2. [Answer 15] If $n$ is a perfect square, it must be of the form $n=p_1^{2a_1}p_2^{2a_2} \dots p_k^{2a_k}$ where $p_i$ are primes and $a_i \in \mathbb{N}$. If $n$ is also a power of 2, it must be of the form $n=2^m$. Equating these, we have $2^m=p_1^{2a_1}p_2^{2a_2} \dots p_k^{2a_k}$. If any of the primes $p_i$ is other than 2, we have a contradiction. Thus, the only prime factor of $n$ can be 2. So we have $n=2^m=2^{2a_1}$, which means $m$ must be an even number. So $n$ can be $2^2=4$, $2^4=16$, $2^6=64$, $2^8=256$, $2^{10}=1024$, $2^{12}=4096$, $2^{14}=16384$, $2^{16}=65536$, $2^{18}=262144$, $2^{20}=1048576$. Of these, only $2^{10}=1024$ has four digits. The next largest would be $2^{20}=1048576$, which has 7 digits. Thus, the number of perfect squares which are powers of 2 and which have at most 4 digits is 5, corresponding to $2^0, 2^2, 2^4, 2^6,$ and $2^8$. Thus, the required number is $1024$. [Answer 16] $1024=2^{10}$ $1024=(2^5)^2=32^2$ So $1024$ is a perfect square. $1024=2^{10}$ So it is a perfect power of 2. The answer is $1024$. [Answer 17] The smallest such integer is 16. If $n$ is a perfect square, then $n=k^2$ for some integer $k$. If $n$ is also a perfect fourth power, then $k^2$ must also be a perfect fourth power. Since $k$ is an integer, the only way for $k^2$ to be a perfect fourth power is if $k$ is itself a perfect square. So we are looking for squares which are also fourth powers, i.e. numbers of the form $m^4$. $1^4=1$ $2^4=16$ $3^4=81$ $4^4=256$ $5^4=625$ $6^4=1296$ $7^4=2401$ $8^4=4096$ $9^4=6561$ $10^4=10000$ The smallest four-digit perfect square that is also a perfect fourth power is $1296$. [Answer 18] I'm not sure if you mean $ n!=n $ or $ n!=n^2 $. If $ n!=n $ then $ n=1 $ or $ n=2 $. If $ n!=n^2 $ then $ (n-1)!=n $. If $ n > 1 $, then $ (n-1)! $ is always even. If $ n=2 $, $ 1!=2 $ which is false. If $ n=3 $, $ 2!=3 $ which is false. If $ n=4 $, $ 3!=6 \neq 4=n $. If $ n=5 $, $ 4!=24 \neq 5=n $. If $ n=6 $, $ 5!=120 \neq 36=n^2 $. If $n=1$, $1!=1=1^2$, so $n=1$ is a solution. Consider the growth rates of $n!$ and $n^2$. When $n=4$, $n!=24$ and $n^2=16$. When $n=5$, $n!=120$ and $n^2=25$. Since $n!$ grows faster than $n^2$ for $n \ge 4$, $n!$ will never equal $n^2$ again. Thus, $n=1$. [Answer 19] Let $n$ be a positive integer such that $2^n+1$ is a perfect square. Let $2^n+1=k^2$ for some integer $k$. Since the RHS is a perfect square, $k$ must be odd. So, $2^n=k^2 - 1=(k-1)(k+1)$ Since $k$ is odd, both $k-1$ and $k+1$ are even. Also, two successive even integers are not powers of 2. Hence, $k=1$ or $k=3$. If $k=1$, $2^n+1=1$, which means $2^n=0$, which is impossible. If $k=3$, $2^n+1=3^2=9$, so $2^n=8=2^3$, giving $n=3$. Thus we have shown that the only integer solution for $n$ is $3$, and we have $2^3+1=9=3^2$. [Answer 20] I’m assuming that $\pi(n)$ refers to the usual prime-counting function, denoting the number of primes less than or equal to $n$. Yes, $\pi(n)$ divides $n$ for infinitely many $n$. We can easily see this by focusing on the numbers slightly less than the primorials $p_1 p_2 \ldots p_k$, where $p_i$ is the $i$th prime. For example, consider numbers of the form $n=6k-1=2 \cdot 3 \cdot k - 1$. Any number of this form is coprime to $2$ and $3$. Thus, every prime factor of $n$ must be of the form $6k \pm 1$. Moreover, it must be smaller than $\sqrt{n}$, and if $n$ is large enough there will be many such primes less than $\sqrt{n}$. The product of these primes will be a divisor of $n-1$, so we have something of the form $n-1=2^a 3^b m$, where $m$ is a product of primes greater than 3. If $n$ is large enough, then there will be enough small primes to choose from that we can find some subset whose product is a square. In particular, consider $n$ of the form $p_k\# - 1$ for some $k$. Then $n-1=p_k\# - 2$, where $p_k\#$ denotes the product of the first $k$ primes. If we choose $k$ large enough, there will be enough divisors of $n-1$ to ensure that at least one of these is a perfect square. This is because the number of divisors grows like 2 to the power of the number of prime factors. For example, if $n=29$, then $n-1=28=2^2 \cdot 7$. We can take $m=14$, which has $\pi(m)=4$ prime factors. Then $n-1=2 \cdot 14$ and $n=2 \cdot 14 + 1=29$. We check and see that $\pi(29)=10$, which is even. If $n=31$, then $n-1=30=2 \cdot 3 \cdot 5$. If $n=47$, then $n-1=46=2 \cdot 23$. If $n=48$, then $n-1=47$, which is prime. In general, we are looking for $n$ such that $n-1$ has an odd number of divisors, or equivalently $\frac{n-1}{2}$ has an odd number of divisors. So $n-1=2 p_1^{a_1} p_2^{a_2} \ldots p_k^{a_k}$ where $p_i$ are distinct odd primes, and each $a_i$ is even. If $n-1=2m^2$ for some integer $m$, then $n=2m^2 + 1$. If we consider $m=2^j q$ for $q$ odd, then $n-1=2^{2j+1}q^2$, where $q$ is some odd number. If $q=1$, then $n-1=2^{2j+1}$, and $n$ is a Fermat number. $n=17$ gives $n-1=16=2^4$, so $n=17$ is such a prime. If $n=3$, we have $3-1=2^1$, so $n=3$ is prime and we have $\pi(3)=2$, which divides $3-1=2$. If $n=5$, $n-1=4=2^2$, so $4 \nmid \pi(5)=3$. If $n=7$, $n-1=6=2 \cdot 3$, so $\pi(7)=4$, which divides $6$. If $n=17$, $n-1=16=2^4$, so $\pi(17)=7$, but $16$ does not divide $7$. If $n=31$, $n-1=30=2 \cdot 3 \cdot 5$, so $\pi(31)=11$, and 30 does not divide 11. If $n=2^m+1$ is prime, then $\pi(n)=\pi(2^m)+1$. If $n=2^m-1$ is prime, then $\pi(n)=\pi(2^m-2)+1$. Consider $n=2^m+1$. $\pi(n) | n-1 \implies \pi(2^m+1) | 2^m$ If $n=2^{11}+1=2049=23 \times 89$, then $\pi(2049)=306$. $2048$ divides $306$ since $306=2 \cdot 3^2 \cdot 17$. Final Answer: The final answer is $\boxed{2}$
因为上帝并非不公义,竟忘记你们的工作和你们为他的名所显的爱心,就是你们过去和现在伺候圣徒的爱心。 我们盼望你们各人都显出同样的热忱,一直到底,好达成所确信的指望。 这样你们才不会懒惰,却成为效法那些藉着信和忍耐承受应许的人。
这不是说我已经得着了,已经完全了;而是竭力追求,或许可以得着基督耶稣所要我得着的。 弟兄们,我不是以为自己已经得着了;我只有一件事,就是忘记背后,努力面前的, 向着标竿直跑,要得上帝在基督耶稣里从上面召我来得的奖赏。
“不是每一个称呼我‘主啊,主啊’的人都能进天国;惟有遵行我天父旨意的人才能进去。 在那日必有许多人对我说:‘主啊,主啊,我们不是奉你的名传道,奉你的名赶鬼,奉你的名行许多异能吗?’ 我要向他们宣告:‘我从来不认识你们,你们这些作恶的人,给我走开!’”
那美好的仗我已经打过了,当跑的路我已经跑尽了,该信的道我已经守住了。 从此以后,有公义的冠冕为我存留,就是按着公义审判的主到了那日要赐给我的;不但赐给我,也赐给凡爱慕他显现的人。
为要他按着他丰盛的荣耀,藉着他的灵,使你们内心的力量刚强起来; 又要他使基督因着你们的信住在你们心里,使你们既在爱中生根立基, 能够和众圣徒一同明白基督的爱是何等的长、阔、高、深,并知道这爱是超过人的知识所能测度的,为要使你们充满上帝一切的丰盛。
“你们要谨慎,免得被贪食、醉酒和今生的忧虑压住你们的心,那日子就忽然临到你们, 如同罗网一样,因为那日子要临到所有居住在地面上的人。 你们要时时警醒,常常祈求,使你们能逃避这一切要来的事,得以站立在人子面前。”
你们不知道在运动场上赛跑的,大家都跑,但得奖赏的只有一人?你们也要这样跑,好使你们得着奖赏。 凡参加竞赛的,在各方面都要有节制,他们不过是要得会朽坏的冠冕;我们却是要得不会朽坏的冠冕。 所以,我奔跑,不像无目标的;我斗拳,不像打空气的。 我克制己身,使它完全顺服,免得我传福音给别人,自己反而被淘汰了。
所以,我们既因信称义,就藉着我们的主耶稣基督得以与上帝和好。 因为我们作仇敌的时候,尚且藉着上帝儿子的死得以与上帝和好,既已和好,就更要因他的生得救了。 不但如此,我们既藉着我们的主耶稣基督得以与上帝和好,也就藉着他以上帝为乐。 为此,正如罪是从一人进入世界,死又从罪而来,于是死就临到所有的人,因为人人都犯了罪。 没有律法之前,罪已经在世上,但没有律法,罪也不算罪。 然而,从亚当到摩西,死就掌了权,连那些不与亚当犯一样罪过的,也在死的权下。亚当是那以后要来之人的预像。 但是过犯不如恩赐,若因一人的过犯,众人都死了,那么,上帝的恩典,与那因耶稣基督一人而来的恩典中的赏赐,岂不加倍地临到众人吗? 因一人犯罪而来的后果,也不如赏赐,原来审判是由一人而定罪,恩赐乃是由许多过犯而称义。 若因一人的过犯,死就因这一人掌权,那些受洪恩又蒙所赐之义的,岂不更要因耶稣基督一人在他们生命中掌权吗? 这样看来,因一次的过犯,所有的人都被定罪;照样,因一次的义行,所有的人也就被称义而得生命了。 因一人的悖逆,众人成为罪人;照样,因一人的顺从,众人也成为义了。 我们又藉着他,因信得以进入现在所站立的这恩典中,并且欢欢喜喜盼望上帝的荣耀。
上帝的神能已把一切关乎生命和虔敬的事赐给我们,因我们认识那用自己荣耀和美德召我们的上帝。 因此,他已把又宝贵又极大的应许赐给我们,使我们既脱离世上从情欲来的败坏,就得分享上帝的本性。
我心里柔和谦卑,你们当负我的轭,向我学习;这样,你们的心灵就必得安息。 问耶稣:“将要来的那位就是你吗?还是我们要等候另一位呢?” 因为我的轭是容易的,我的担子是轻省的。”
然而,靠着爱我们的主,在这一切的事上,我们已经得胜有余了。 因为我深信,无论是死,是活,是天使,是掌权的,是有权能的 ,是现在的事,是将来的事, 是高处的,是深处的,是别的受造之物,都不能使我们与上帝的爱隔绝,这爱是在我们的主基督耶稣里的。
“那时,天国好比十个童女拿着灯出去迎接新郎。 她们去买的时候,新郎到了。那预备好了的,与他进去共赴婚宴,门就关了。 其余的童女随后也来了,说:‘主啊,主啊,给我们开门!’ 他却回答:‘我实在告诉你们,我不认识你们。’ 所以,你们要警醒,因为那日子,那时辰,你们不知道。”