Problem: Problem F: Farey Sequence

slip likes to look at the numbers. Just looking at the remaining time while downloading the file is enough to kill the time. Such a slip was taught an interesting sequence by a friend. The definition of the sequence is as follows.

The general term is expressed as Fn. Fn is an arrangement of all reduced fractions (irreducible fractions) from 0 to 1 with a denominator of n or less, in ascending order. However, the integers 0 and 1 are treated as fractions 0/1 and 1/1, respectively.

So F3 is


F3 = (0/1, 1/3, 1/2, 2/3, 1/1)


It is expressed as.

If F5


F5 = (0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1)


It is expressed as.

slip quickly fell in love with this sequence. However, even looking at these sequences, I couldn't quite grasp the characteristics. In order to grasp the characteristics, I first tried to find out how many terms there were in each term, but I didn't understand the rules for how to increase them, so I gave up trying to understand them on my own.

Therefore, I decided to ask you, who thinks you are a friend, how many terms there are in the specified terms. Your job is to find the number of terms in a given term.

Input

The input is given in the following format.


t
n1
...
ni
...
nt


t (1 ≤ t ≤ 10000) is the number of test cases. ni (1 ≤ ni ≤ 1000000) is the number of the given term.

Output

Display the number of terms on one line for each test case.

Sample Input


2
3
Five



Output for Sample Input


Five
11






Example

Input

2
3
5


Output

5
11

Solution (in CPP):

Solution:
#pragma GCC optimize ("O3")

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <queue>
#include <set>
#include <algorithm>
#include <numeric>
#include <list>
using namespace std;

using QWORD  = uint64_t;
using SQWORD = int64_t;
using DWORD  = uint32_t;
using SDWORD = int32_t;
using WORD   = uint16_t;
using SWORD  = int16_t;
using BYTE   = uint8_t;
using SBYTE  = int8_t;
using DOUBLE = double;
using FLOAT  = float;

#define MIN_SDWORD (-2147483648)
#define MAX_SDWORD (2147483647)
#define MIN_SBYTE (-128)
#define MAX_SBYTE (127)

#define MIN_SQWORD (0x8000000000000000)
#define MAX_SQWORD (0x7FFFFFFFFFFFFFFF)

#define MAX_QWORD  (0xFFFFFFFFFFFFFFFF)
#define MAX_DWORD  (0xFFFFFFFF)
#define MAX_WORD   (0xFFFF)
#define MAX_BYTE   (0xFF)


#define ArrayLength(a)  (sizeof(a) / sizeof(a[0]))

static inline QWORD MAX(QWORD a, QWORD b) { return a > b ? a : b; }
static inline DWORD MAX(DWORD a, DWORD b) { return a > b ? a : b; }
static inline SDWORD MAX(SDWORD a, SDWORD b) { return a > b ? a : b; }
static inline QWORD MIN(QWORD a, QWORD b) { return a < b ? a : b; }
static inline DWORD MIN(DWORD a, DWORD b) { return a < b ? a : b; }
static inline SDWORD MIN(SDWORD a, SDWORD b) { return a < b ? a : b; }

#define BYTE_BITS   (8)
#define WORD_BITS   (16)
#define DWORD_BITS  (32)
#define QWORD_BITS  (64)

using M_BOOL = bool;
#define M_TRUE (true)
#define M_FALSE (false)
#define DIVISOR (1000000007)

static inline void inputString(char *pcStr)
{
    char *pcCur = pcStr;
    for (;;) {
        char c = getchar();
        if (('\n' == c) || (EOF == c)) {
            break;
        }
        *pcCur = c;
        pcCur++;
    }
    *pcCur = '\0';
}


static inline SQWORD inputSQWORD(void)
{
    SQWORD sqNumber = 0;
    SQWORD sqMultiplier = 1;
    M_BOOL bRead = M_FALSE;
    for (;;) {
        char c = getchar();
        if (!bRead) {
            if ('-' == c) {
                sqMultiplier = -1;
            }
        }
        if (('0' <= c) && (c <= '9')) {
            sqNumber *= 10LL;
            sqNumber += (SQWORD)(c - '0');
            bRead = M_TRUE;
        } else {
            if (bRead) {
                return sqNumber * sqMultiplier;
            }
        }
    }
}


static inline SDWORD inputSDWORD(void)
{
    SDWORD lNumber = 0;
    SDWORD lMultiplier = 1;
    M_BOOL bRead = M_FALSE;
    for (;;) {
        char c = getchar();
        if (!bRead) {
            if ('-' == c) {
                lMultiplier = -1;
            }
        }
        if (('0' <= c) && (c <= '9')) {
            lNumber *= 10;
            lNumber += (c - '0');
            bRead = M_TRUE;
        } else {
            if (bRead) {
                return lNumber * lMultiplier;
            }
        }
    }
}

static inline DOUBLE inputFP(void)
{
    DOUBLE dInt = 0.0;
    DOUBLE dFrac = 0.0;
    DOUBLE dMultiplier = 1.0;
    DWORD dwFpCnt = 0;
    DOUBLE *pdCur = &dInt;
    M_BOOL bRead = M_FALSE;
    for (;;) {
        char c = getchar();
        if (!bRead) {
            if ('-' == c) {
                dMultiplier = -1;
            }
        }
        if ('.' == c) {
            pdCur = &dFrac;
        } else if (('0' <= c) && (c <= '9')) {
            (*pdCur) *= 10;
            (*pdCur) += (DOUBLE)(c - '0');
            bRead = M_TRUE;
            if (pdCur == &dFrac) {
                dwFpCnt++;
            }
        } else {
            if (bRead) {
                return dMultiplier * (dInt + dFrac / (pow((DOUBLE)10.0 , (DOUBLE)dwFpCnt)));
            }
        }
    }
}


/**
 *  mod による操作ライブラリ
 */

#define ANS_MOD (1000000007LL)
 
static SQWORD addMod(SQWORD x, SQWORD y)
{ 
    return (x + y) % ANS_MOD;
}
 
static SQWORD subMod(SQWORD x, SQWORD y)
{
    return (x - y + ANS_MOD) % ANS_MOD;
}
 
static SQWORD mulMod(SQWORD x, SQWORD y) 
{
    return (x * y) % ANS_MOD;
}
 
static SQWORD powMod(SQWORD x, SQWORD e) {
    SQWORD v = 1;
    for (; e; x = mulMod(x, x), e >>= 1) {
        if (e & 1) {
            v = mulMod(v, x);
        }
    }
    return v;
}
 
static SQWORD divMod(SQWORD x, SQWORD y)
{
    return mulMod(x, powMod(y, ANS_MOD - 2));
}
 
 
static SQWORD combMod(SQWORD n, SQWORD k)
{
    SQWORD v=1;
    for(SQWORD i=1; i<=k; i++) {
        v = divMod(mulMod(v, n-i+1),i);
    } 
    return v;
}

#define MAX_N   (1000000LL)
//#define MAX_N   (200LL)

static void getPrimes(vector<SDWORD> &vlPrimes, SDWORD lMax)
{
    /* lSearchMax と ループ内の *2 の関係から、入力は3以上とすること */
    if (!(1 <= lMax)) {
        printf("Oops!");
        return;
    }

    /* 素数のリストを作る */
    vector<bool> vbIsPrime(lMax + 1, true);
    SDWORD lSearchMax = sqrt(lMax) + 1;
    vbIsPrime[0] = false;
    vbIsPrime[1] = false;
    for (SDWORD lPrime = 2; lPrime < vbIsPrime.size(); lPrime++) {
        if (vbIsPrime[lPrime]) {
            vlPrimes.emplace_back(lPrime);
            if (lPrime <= lSearchMax) {
                for (SDWORD lCurNum = lPrime * 2; lCurNum <= lMax; lCurNum += lPrime) {
                    vbIsPrime[lCurNum] = false;
                }
            }
        }
    }
}    


int main(void)
{
    vector<SDWORD> vlPrimes;

    getPrimes(vlPrimes, MAX_N);

    static set<pair<SQWORD, SQWORD>> vMutuallyPrimeNums;
    static SDWORD s_alMutuallyPrimeNum[MAX_N + 1];
    static vector<pair<SQWORD, SQWORD>> vpairAddMP;
    for (SDWORD lIdx = 0; lIdx < ArrayLength(s_alMutuallyPrimeNum); lIdx++) {
        s_alMutuallyPrimeNum[lIdx] = 0;
    }

    /* オイラー関数を計算する */
    vMutuallyPrimeNums.insert(make_pair(1, 1));
    for (auto prime: vlPrimes) {
        vpairAddMP.clear();

        /* 素数 */
        auto it = vMutuallyPrimeNums.begin();
        while (it != vMutuallyPrimeNums.end()) {
            SQWORD sqNextNum = it->first * (SQWORD)prime;
            SQWORD sqMPCount = it->second;
            for (SQWORD sqPow = 1; sqNextNum <= (SQWORD)MAX_N; sqNextNum *= (SQWORD)prime, sqPow++) {
                if (1 == sqPow) {
                    sqMPCount *= (prime - 1);
                } else {
                    sqMPCount *= prime;
                }
                s_alMutuallyPrimeNum[sqNextNum] = sqMPCount;
                vpairAddMP.emplace_back(make_pair(sqNextNum, sqMPCount));
            }
            if (MAX_N / prime < it->first) {
                vMutuallyPrimeNums.erase(it, vMutuallyPrimeNums.end());
                break;
            } else {
                ++it;
            }
        }
        for (auto addMP: vpairAddMP) {
            vMutuallyPrimeNums.insert(addMP);
        }
    }

    /* Cumsum */
    static SQWORD s_asqAnswers[MAX_N + 1];
    s_asqAnswers[1] = 2;
    for (SQWORD sqNum = 2; sqNum < ArrayLength(s_asqAnswers); sqNum++) {
        s_asqAnswers[sqNum] = s_asqAnswers[sqNum - 1] + (s_alMutuallyPrimeNum[sqNum]);
    }

    /* Query */
    SDWORD lInput_Q = inputSDWORD();
    for (SDWORD lQueryIdx = 0; lQueryIdx < lInput_Q; lQueryIdx++) {
        SDWORD lInput_N = inputSDWORD();
        printf("%lld\n", s_asqAnswers[lInput_N]);
    }
    return 0;
}