  We have carried out a study of the interstellar medium (ISM) toward a
shell-like supernova remnant SNR Puppis A by using the NANTEN CO and ATCA HI
data. We synthesized a comprehensive picture of the SNR radiation by combining
the ISM data with the gamma-ray and X-ray distributions. The ISM, both atomic
and molecular gas, is dense and highly clumpy, and is distributed all around
the SNR, but mainly in the north-east. The CO distribution revealed an enhanced
line intensity ratio of CO($J$ = 2-1)/($J$ = 1-0) transitions as well as CO
line broadening, which indicate shock heating/acceleration. The results support
that Puppis A is located at 1.4 kpc, in the local arm. The ISM interacting with
the SNR has a large mass of $\sim$10$^{4}$ $M_{\odot}$ which is dominated by
HI, showing good spatial correspondence with the Fermi-LAT gamma-ray image.
This favors the hadronic origin of the gamma-rays, while additional
contribution of the leptonic component is not excluded. The distribution of the
X-ray ionization timescales within the shell suggests that the shock front
ionized various parts of the ISM at epochs ranging over a few to ten 1000 yr.
We therefore suggest that the age of the SNR is around 10$^{4}$ yr as given by
the largest ionization timescale. We estimate the total cosmic ray energy
$W_{\rm p}$ to be 10$^{47}$ erg, which is well placed in the cosmic-ray
escaping phase of an age-$W_{\rm p}$ plot including more than ten SNRs.
