//
// Convert a formula from direct polish notation
// into the normal (infix) form
//
// Grammar:
// S -> + S S | - S S | * S S | / S S |
//      a | b | ... | z | A | B | ... | Z
//
// Example: on input
//     / + a b - a b
// the program prints
//     ((a+b)/(a-b))
#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <setjmp.h>

static char line[1024] = "";
static char *curpos = line;

static char outLine[1024];
static char *outpos = outLine;

static void parse_S0();
static void parse_S();

static void skipSpace();
static void syntaxError(const char* s);
static void output(char c);
jmp_buf env;

int main() {
    while (true) {
        setjmp(env);
        printf("Input a formula in the direct polish notation:\n");
        fgets(line, 1022, stdin);

        int lineLen = strlen(line);
        if (lineLen >= 1 && line[lineLen-1] == '\n') {
            --lineLen; line[lineLen] = 0;
        }
        if (lineLen >= 1 && line[lineLen-1] == '\r') {
            --lineLen; line[lineLen] = 0;
        }
        if (lineLen == 0)
            break;

        curpos = line;
        skipSpace();
        if (*curpos == 0)
            break;

	// Add the end marker
        line[lineLen] = '$'; ++lineLen;

        outpos = outLine;

        parse_S0();

        *outpos = 0;
        printf("%s\n", outLine);
    }
    return 0;
}

static void parse_S0() {
    parse_S();

    // Check the end marker
    skipSpace();
    if (*curpos != '$')
        syntaxError(curpos);
}

static void parse_S() {
    skipSpace();

    char c = *curpos;
    switch (c) {
    case '+':
    case '-':
    case '*':
    case '/':
        ++curpos;        // Skip an operation
        output('(');     // Enclose a formula into parentheses
        parse_S();       // Parse the first operand
        output(c);       // Print an operation
        parse_S();       // Parse the second operand
        output(')');     // Close parentheses
        break;
    default:
        if (isalpha(c)) {
            output(c);  // Print a name
            ++curpos;   // Skip a name
        } else {
            syntaxError(curpos);
        }
    }
}

static void skipSpace() {
    while (*curpos != 0 && isspace(*curpos))
        ++curpos;
}

static void output(char c) {
    if (outpos - outLine >= 1023)
        return;
    *outpos = c; ++outpos;
}

static void syntaxError(const char *str) {
    if (*str != 0)
        printf("Syntax error: \"%s\"\n", str);
    else
        printf("Syntax error.\n", str);

    longjmp(env, 0);
}