template 질문입니다.

//tminmax3.h

template< typename T > T max( T a, T b )
{
    return ( a > b ) ? a : b;
}

template< typename T > T min( T a, T b )
{
    return ( a < b ) ? a : b;
}

//tfunc3.cpp
#include <iostream>
#include "tminmax3.h"

using namespace std;

double mid( double, double );

int main ( void )
{
    cout << "최소값: " << min( 123, 456 ) << endl;
    cout << "최대값: " << max( 123, 456 ) << endl;
    cout << "중간값: " << mid( 123, 456 ) << endl;
    
    return 0;
}

//mid.cpp

#include "tminmax3.h"

double mid( double a, double b )
{
    return ( min( a, b ) + max( a, b ) ) / 2.;
}

컴파일을 해보면...다음과 같은 에러가 납니다.

tminmax3.h:7: candidates are: T min(T, T) [with T = int]
/usr/include/c++/3.2.2/bits/stl_algobase.h:149:                 const _Tp&
   std::min(const _Tp&, const _Tp&) [with _Tp = int]
tfunc3.cpp:11: call of overloaded `max(int, int)' is ambiguous
tminmax3.h:2: candidates are: T max(T, T) [with T = int]
/usr/include/c++/3.2.2/bits/stl_algobase.h:169:                 const _Tp&
   std::max(const _Tp&, const _Tp&) [with _Tp = int]