Automatic nutrient estimator: distributing nutrient solution in hydroponic plants based on plant growth

Block diagram

Hydroponics is soilless cultivation that can be grown in any small indoor area. Each requirement must be provided artificially in a controlled environment, whereas everything is naturally available for soil agriculture. The above Fig. 2 depicts the whole idea of our proposed system.

Our proposed system aims at developing an auto-dosing system for nutrient management to distribute essential nutrients for plants with less human intervention. The system mainly automates the nutrient supply to prevent under-dosing or overdose. This system calculates and estimates the number of nutrients based on the ratios given at every plant stage or age. The block diagram of the system mainly comprises a growing chamber, water reservoir, NPK mixture pumps, and Arduino microcontroller that connects various sensors to sense different parameters like pH, EC, temperature, and water levels and uses LCD 16 × 2 monitor to display all these parameters.

The pH and EC sensors in the system continuously monitor the hydroponic solution. If the recorded pH falls beyond the required range, the system triggers pH adjustment processes, such as introducing pH-up or pH-down solutions, to return the pH to the ideal range. If the EC values exceed the predefined thresholds, the system adjusts the nutrient content by diluting the solution with water or supplementing it with more nutrients. These corrective steps are frequently automated and initiated in real-time to handle any variations as quickly as possible and to guarantee that the nutrient solution remains within the precise parameters conducive to plant health. The system provides a stable and controlled environment by proactively maintaining pH and EC levels, protecting against harmful impacts on nutrient uptake and overall plant development in hydroponic farming. It feels pH and EC in regular intervals and compares recorded values with the minimum threshold already initialized in the system. EC and pH ranges vary from plant to plant. The nutrient solution requirement of the plant is directly dependent on the growth stage of the plant, which causes EC ranges to go for different growth stages. If the observed pH value is outside the predefined range, remedial measures are being taken to restore a workable pH range. As well as it is checking whether the recorded EC value is higher, lower, or feasible. If recorded EC values are higher, switch on the water pump to reduce the nutrient concentration. On the other hand, if ppm goes down, change on NPK mixture pumps to increase the nutrients in the reservoir.

The Growth Stage Identification algorithm is a sophisticated mechanism that determines the developmental phases of plants in a hydroponic environment, ensuring exact nutrient administration adapted to each growth stage. This program uses multiple data sources to make informed conclusions about the plant’s age. Environmental sensors, such as those that measure temperature, humidity, and light intensity, provide real-time information on growing conditions. Furthermore, nutrient sensors monitor the composition of the hydroponic solution, providing information about the plant’s nutritional requirements. This abundance of data is processed by the algorithm, which then applies programmed growth patterns appropriate to the farmed plant species. These patterns, which range from germination to vegetative growth, blooming, and fruiting, serve as a guide for determining the present stage of growth. Machine learning techniques are used in some implementations to improve the algorithm’s capabilities by learning from prior data and adjusting to changing environmental conditions. The decision-making mechanism of the algorithm causes the dosing system to distribute the correct amount and composition of nutrients based on the recognized growth stage. In hydroponic farming practices, this dynamic and adaptable technique guarantees that plants receive personalized nourishment throughout their lifecycle, optimizing their health and productivity. While supplying nutrients, the system executes the Growth Stage Identification algorithm to identify the age of the plant and provide the correct quantity of nutrients accordingly. NPK pumps continue flowing nutrient solution for the period calculated in Eqs. (1), (2), or (3) according to the plant stage.

The View at Site app connects the autonomous dosing system to the farmer’s mobile smartphone, allowing rapid access to important information. The IoTCloudData cloud server collects and processes data from the hydroponic setup as a centralized hub. The farmer may remotely monitor critical variables such as nutrient levels, pH, and environmental conditions via the app. The system sends data on these parameters to the cloud server in real time, and the View at Site app retrieves it and displays it on the farmer’s mobile device in an easily understandable way. Furthermore, the app allows the farmer to set and alter dosing parameters, receive notifications when conditions deviate from ideal, and even remotely manage the dosing system. This use of IoT technology not only streamlines the monitoring process, but also provides farmers with the freedom and convenience to operate their hydroponic systems efficiently and proactively, hence improving the precision and productivity of their farming practices. The hydroponic system ensures a dynamic understanding of the plant’s immediate surroundings by tracking these parameters in real-time. This information is then processed by algorithms or control systems that use established growth patterns for the individual plant type. The system can properly estimate the current growth stage of the plants by aligning the observed parameters with these growth patterns. This data directs the automated dosing system to distribute the precise amount and composition of nutrients required at each developmental stage, encouraging strong plant health and, ultimately, maximizing potential production in hydroponic farming.

Circuit diagram

The components of the circuitry proposed system have shown in File S1, including

• Step down transformer for power supply

• Arduino UNO

• Relay board with submersible pumps for pumping water and nutrients

• pH sensor

• EC sensor

• DHT11 sensor for measuring temperature

• Ultrasonic sensor

• 20 × 4 LCD

• MCP3008 10-bit ADC

1. DHT11 sensor: DHT11 low-cost digital sensor used in growing hydroponics to measure air temperature and humidity. It usually operates at 3.5 to 5.5 V and can measure temperatures up to 500 C.

2. Arduino UNO: A microcontroller used to connect input-output devices, sensors, and other required electrical devices. It supports the IDE environment to a program to the system with any high-level languages or packages like Python. The power supply with 5 Volts is used to supply power to the board and all the sensors.

3. Relays pumping water and nutrients: A relay is an electrical device that behaves like a switch for pumping water and nutrients into our system. It allows you to switch on or off pumps in regular intervals effortlessly. Totally four relays used in our approach to control water, nutrients, and pH solutions. Each relay has three terminals at the low current side, namely VCC, GND, and IN pins, and three at the high current side NO, C, and NC. The IN pin, connected to Pin 7 in the Arduino board, causes the relay to switch the pump ON or OFF.

4. pH meter: pH is the potential of hydrogen that tells how well plants absorb nutrients. The pH meter calibrates the acidity or alkalinity of nutrient explanation in the water tank. In this system, we have grown tomato plants for the experimental results, and tomato plants can grow at a 5.5 to 6.5 feasible pH range. At all times, pH should be checked after getting EC in the predetermined range. The pH is too low or too high can stop nutrient uptaking and causes some deficiencies in plants. We should use pH up or down solutions to bring into the correct pH ranges.

5. EC meter: EC meter and pH meter supports feeding hydro plants nutrients at consistent levels. Electrical conductivity (EC) can be measured in millisiemens (mS) or parts per million (ppm). For tomato plants, optimal EC ranges can be from 2 to 5 mS or 1,400 to 3,500 ppm levels based on the type of crops and growth stage of the tomato plants. If the EC value decreases, plants consume soundly and switch ON NPK pumps to raise nutrient solution. If the solution’s EC goes up, it means more nutrients in the resolution, and switching to the ON water pump dilutes the solution.

6. Ultrasonic sensor: An ultrasonic sensor (HC SR04) is used to regulate the water level in the water tank. It is used to degree distance from one object to another object. It controls the water pump to turn on or off, thus avoiding water wastage. If the water equal recorded is less than the inception, it prompts the water pump to turn ON; otherwise, it will turn OFF immediately.

7. 20 × 4 LCD: We used 20 columns × 4 rows of character LCD monitor designed for Arduino microcontroller with 16 pins to display all the input from sensors.

8. ATMEGA328 ADC: This device used for analog to digital conversion and vice versa.

Tomato plant at germination stage

At the time of the seedling or germination stage, the plant supplied nutrients naturally available in the RO water. The seedling can start its growth with lightening, CO₂, oxygen, and minimal nutrients.

Tomato plant at vegetative stage

N-P-K ratios represent the percentage of each nutrient in the solution. For example, the N-P-K ratio 7-9-5 is the best ratio at the vegetative stage that contains 7% of nitrogen, 9% of phosphorous, and 5% of potassium. The remaining solution is filled with varying amounts of micronutrients.

During the vegetative stage, plants consume higher amounts of nitrogen in the fertilizer for a rapid growth rate. Nutrient consumption with more nitrogen products makes plants healthier, with leaves seen dark shined greenish. At this stage, plants take around 1,400 to 2,000 ppm of nutrients required for growth. In our system, the minimum threshold of 1,400 ppm and a maximum of 2,000 ppm are taken for nutrient estimation.

Tomato plant at reproductive stage (flower/fruit stage)

Plants’ reproduction stage starts with flowers that carry out reproductive functions to produce fruits. During this stage, plants consume higher amounts of phosphorous (P) for flower/fruit production and reduce taking nitrogen as it is already collected in vegetative stage at higher levels. Phosphorous is also needed for healthy root structure development. In this stage, potassium is a crucial nutrient for reproduction. In this stage, a 5-15-14 NPK ratio may be a wise choice for plant growth. Plants require around 2,000 to 4,500 ppm of nutrients for optimum growth throughout the blooming or fruiting periods. In our system, the minimum threshold of 2,000 ppm and a maximum threshold of 2,500 ppm has taken. Similarly, for the fruiting stage, the minimum threshold of 2,200 ppm and ultimate point of 3,500 ppm has been accepted for nutrient estimation. Achieving 97.5% accuracy in recognizing the vegetative stage, 97.5% in the blooming stage, and 99.4% in the fruiting stage in hydroponic plants using nutrient solutions has significant implications for precision agriculture. This level of precision enables focused and efficient fertilizer delivery throughout the plant’s growth cycle, optimizing resource efficiency and minimizing waste. With the potential to improve crop health and productivity, such accuracy contributes to the automation of hydroponic systems, decreasing labor requirements and enabling for data-driven decision-making. Furthermore, the environmental benefits, such as reduced nutrient runoff and a smaller ecological imprint, correspond with sustainable farming practices. This high level of precision not only ensures crop consistency, but also presents hydroponic farming as a competitive and environmentally aware strategy in modern agriculture.

Equations for nutrients estimation based on the stage

Estimating and calculating the ratios of nutrients to add to nutrient solutions is a primary issue in the hydroponic controlled environment. In India, the hydroponics culture is beginning. Most urban people are aware of growing hydroponics. In this urban farming, a farmer is tightly engaged with his day schedules. They cannot be time-intensive in dosing plants and making pH or EC adjustments. And if he is new to farming, he may accidentally shock his plants by over- or under-dosing.

Overdosing on nutrients can result in a nutritional burn, the creation of salt content, and even plant death. Underdosing of nutrients sometimes results in plant decreases. The use of automated dosing systems is the solution to this problem. This system is used to avoid human errors and simplify nutrient management with less human intervention (dosing, checking levels, measuring pH and EC).

Normally EC is measured in millisiemens. We can convert this EC to ppm using 500 NaCl or 700 KCl scales.

$$\begin{gathered} 1MS=500ppm=EC500\left(or\right) \\ 1MS=700ppm=EC\times 700 \end{gathered}$$

For the tomato plant, the optimal EC range is from 2 to 5 mS, i.e., 1,400 to 3,500 ppm, according to the KCl scale. We already discussed that plant absorbing nutrients involves several factors such as on plant stage, type of plant, and plant part growing. Accordingly, nutrient consumption at the vegetative stage is different from the flower stage, and similarly, nutrient uptaking at the flower stage is different from the fruit stage. At the germination stage, the plant uses a tiny percentage of nutrients as it can grow with nutrients available in fresh RO water. When it has grown in 30–40 days, leaves increase with height, around 20 to 30 cm. This stage is called the early vegetative stage. The plant expenses around 1,400 to 2,000 ppm of mixed macro and micronutrients for its happy growth. In this entire stage, the plant consumes more nitrogen with around a 7-9-5 NPK ratio. That means the tomato plant takes 7% of nitrogen, 9% of phosphorous, and 5% of potassium out of the total nutrients provided. Our system continuously measures pH and EC values in a growing environment. If EC measured is less than the minimum threshold at the vegetative stage, then the system immediately switches on NPK pumps for the time Tveg micro seconds.

(1) $$Tveg={\displaystyle \frac{CX\left(MAXVEGppm-SURppm\right)}{FR}}$$

Here, C is the capacity of the nutrient reservoir. MAXVEGppm is the maximum limit of nutrients needed for tomato plants at the vegetative stage, SURppm is surplus ppm of nutrients available in the nutrient reservoir. FR is flowing pump rate. Next to the vegetative stage, plants begin reproduction and flowering in 40–65 days, called the flower stage. In this stage, the plant expenses around 2,000 to 4,500 ppm of mixed macro and micronutrients for healthy growth. In this stage, the plant consumes less nitrogen but more phosphorous and potassium with around a 5-15-14 NPK ratio. That means the tomato plant takes 5% of nitrogen, 15% of phosphorous, and 14% of potassium out of the total nutrients provided. When the system finds an EC range below the minimum threshold, it is necessary to switch on NPK pumps for Tflow ms. The same calculation is done at the fruiting stage with a point change.

(2) $$Tflow={\displaystyle \frac{CX\left(MAXFLOWppm-SURppm\right)}{FR}}$$

(3) $$Tfru={\displaystyle \frac{CX\left(MAXFRUppm-SURppm\right)}{FR}}$$

Here, C is capacity of nutrient reservoir.

MAXFLOWppm is the maximum limit of nutrients needed for tomato plants at the flowering stage,

MAXFRUppm is the maximum limit of nutrients needed for tomato plants at the fruiting stage,

SURppm is surplus ppm of nutrients available in the nutrient reservoir.

FR is flowing pump rate.

The tomato plants start to fruit. It is a very crucial stage, and constant attention is needed. In this Fruit stage, plants’ nutrient consumption equals the flowering stage. When EC recordings are not optimal, then it is required to switch on NPK pumps for the time Tfru.

Automatic nutrient dosing system

Anything that causes plants to be under stress may be due to high temperatures or low lightening, which reduces nutrient usage. At the same, plants keep changing various types of nutrients and nutrient ratios as their rate of growth changes. Due to these reasons, continuous monitoring is needed to check plant nutrient absorption and EC levels. Our developed system can function in both monitoring and dosing plants. The system uses sensors to regularly measure the nutrient reservoir’s pH, EC levels, and temperature ranges. And we are using the Growth Stage Identification algorithm to identify the plant’s growth stage in its life cycle. Hydroponic systems depend on an exact ratio of micronutrients, phosphorus, potassium, and nitrogen, with suggested amounts based on the crop being grown. Real-time data from sensors measuring EC, pH, and nutrient concentrations in the nutrient solution is interpreted by the automatic dosing system. The system dynamically modifies the dosage of nutrient solutions to maintain them within the preset optimal ranges in response to these readings. In addition to doing away with the necessity for manual adjustments, this automated and responsive method guarantees that plants get the exact nutrients they need at every stage of growth, encouraging healthier plants and optimizing crop yield in hydroponic farming.

Procedure for nutrient estimator with visual representation

The Arduino board serves as the main controller of a hydroponic dosing system, coordinating the accurate dispensing of nutrients according to the surrounding conditions. Its central component is the microcontroller, usually an ATmega328p, which runs the programming that defines the logic of the dosing system. Antenna pins interact with sensors that measure factors like pH or nutrition levels, while digital pins are set as outputs to control dosing components, including pumps or valves. Both types of pins are crucial. For reliable performance, the voltage regulator guarantees a steady power supply, and the crystal oscillator gives precise timing for the microcontroller’s functions. Programming and interacting with external devices are made easier via the USB interface. Programmed logic, in which the microcontroller interprets sensor inputs, decides on the basis of specified criteria, and outputs signals to control dosing components, is what makes the dosing system work. The Arduino board functions as a flexible and effective controller thanks to the dynamic interplay of its parts, guaranteeing the accurate and automated distribution of nutrients in hydroponic farming.

The automatic dosing system consists of an Arduino board with a DHT11 temperature sensor, pH, and EC meter. We use a water tank filled with RO water, as in the deep-water culture model, with an aerator supplying oxygen for roots. We must start the system with the required pH range between 5.5 to 6.5 and EC values between 2 to 5. We used submersible pumps for pumping water and nutrients. The amount of time the PUMP is ON or OFF depends on the stage of the plant, pump speed, tank volume, and the number of plants. The programmed Arduino microcontroller periodically records updated values and adjusts the system with pH and EC as per thresholds. It captures the image of the plants to identify the current growth stage at regular intervals. It then stores all the measured data in the IOTCloudData web server that helps the farmer to feed plants with the right amount of nutrients and supplements. Figures 3 and 4 show the flowchart of the nutrient hydroponic automatic controlling system. We programmed our dosing system to adjust between ratios of nutrients for different stages in plant development. Suppose the system is unsuitable for plants with violated pH or EC values. The controller immediately responds and activates an appropriate relay to correct pH or EC to the preferred values. Total four relays with four pumps

• Pump 1 with Relay 1 to fill the water tank

• Pump 2 with Relay 2 to pump nutrients A

• Pump 3 with Relay 3 to pump nutrients B

• Pump 4 with Relay 4 to drain the water tank

The systems adjust 5V DC submersible pumps flowing time using Eq. (2) based on the plant’s growth stage.

FLOWCHART

There are several types of hydroponic systems. Here in this system, deep water culture has been followed for growing plants. This entire setup is designed with a growing medium. This water reservoir is connected with nutrient mixture pumps and an aerator machine to provide oxygen to the bottom of the root. Our hydroponic system is connected to the Arduino microcontroller, which is connected to sensors that sense various features such as temperature, pH, and EC in regular intervals. Every time after sensing, measured values are compared with threshold values already set in the system. Initially, a water level sensor called an ultrasonic sensor is fixed on the microcontroller, checking whether the water is overflowing or underflowing. If the water equal is less than the threshold level, the water pump is on immediately. Once the water level reaches the specified level, it turns off the water pump. If pH is low and less than the pHLow, switch on the water pump to reduce the acidic nature. Otherwise, if pH is more than pHHigh, add some pH corrective solution called citric acid to reduce the basicity. To adjust EC, if it finds EC measured is higher than the ECHigh, water is added to balance the nutrient solution. Otherwise, if the calculated EC value is lower than the threshold range specified, ECLow, then call the Growth Stage Identification algorithm to determine the current plant growth stage and add the nutrient solution for the estimated time. The estimation of nutrients to pump in the system and the amount of time needed to pump the answer is pictorially shown in Fig. 4.

The application of the growth stage identification algorithm in hydroponic farming

The application of the Growth Stage Identification algorithm in hydroponic farming situations has produced significant improvements in a variety of real-world applications. The precise detection of growth stages by the algorithm led to optimal nutrient administration in a tomato-growing commercial greenhouse, minimizing nutrient waste and increasing yield. By automating the procedures of monitoring and fertilizer correction based on accurate growth stage recognition, the algorithm improved labor productivity in vertical farming systems and streamlined operations. Additionally, the algorithm’s use in sustainable urban agriculture practices shown how it may reduce environmental impact by optimizing nutrient solutions, satisfying consumer demand for environmentally friendly food. Scholarly establishments applying the algorithm saw enhanced crop quality as a result of precise nutrient distribution, while arid-region hydroponic farms took use of its potential for resource-efficient farming. Furthermore, the algorithm’s applicability to automated home hydroponics showed that even city people could use it to produce plants successfully and optimally. All of these case studies highlight how adaptable and powerful the Growth Stage Identification algorithm is for raising production, sustainability, and efficiency in a range of hydroponic farming scenarios.

System setup

The proposed system has been implemented to estimate the extra nutrients required to feed the plants in the right amounts. Files S2 and S3 show the system implementation in real-time for visualizing plant growth from vegetative to fruit.

The above experiment used deep water culture to grow the plants in a fixed water tank mixed with the initial amount of nutrients. The tomato plants are taken for demo and monitored from the seedling stage to the fruiting stage for nearly 115 days. The plants were in the observation to analyze that nutrient consumption changes as they change their growth stage.

We used an Arduino board designed with a pH sensor, TDs sensors, and a temperature sensor connected to the outside world using ESP-32 Wi-Fi for automating the nutrient supply. The Arduino board is coded using the software Arduino IDE for the above implementation. Its user-friendly open-source software contains a text editor for writing and uploading data to the board. In this software, most of the components are written and validated using JavaScript. The board stores all the data logs processed and communicates with a private IOTCloudData server connected with an integrated ESP-32 Wi-Fi module.

Plant growth identification

In this system, we automated nutrient supply according to the plant stage. This idea was implemented using the Plant Growth Identification algorithm to record the plant’s maturity. The experimental results of the growth stage identification method showed that it was very accurate and reliable. An impressive 97.5% of the time, the program correctly identified the vegetative stage, showing that it is good at telling the difference between early growth stages. Furthermore, the accuracy stayed high during the flowering stage at 97.5%, showing that the algorithm is reliable at picking up on small changes in plant growth. It was during the fruiting stage that the accuracy rate was the highest, hitting an amazing 99.4%. This exceptional accuracy shows how well the algorithm can exactly pinpoint the complex physiological changes that happen during fruit development. Correlations between the algorithm’s accuracy rates and the nutrient solutions’ parts per million (ppm) values further proved that it was reliable. This showed that accurate growth stage identification and targeted nutrient delivery in the hydroponic system worked well together. It used USB to RS-232 cable to update data from the laptop to the cloud server IOTCloudData. This algorithm successfully detected the plant stages with 99.9% accuracy. The tomato plant images are captured using a camera at the farming site, and some of the photos are taken from Kaggle datasets for training and testing. We use Python programming language to implement this algorithm. TensorFlow and Keras, and Numpy libraries are used for implementation. The algorithm implementation is shown for identifying vegetative, flowers, and fruit in Files S4–S6, respectively.

Estimating and automating nutrient supply

The Arduino board connected the water tank with nutrient bottles A and B to supply the estimated amount of nutrients calculated. Based on the data received from sensors, the controller processes the data and sends instructions to the actuator to turn on Nutrient A and Nutrient B pumps for the amount of time calculated using the above equations with input parameters plant stage, tank volume, and surplus amount of nutrients required at that stage.

For example: Assume plants are at the flowering stage, and the measurement of nutrients in the 15-l water tank was reduced to 1,700 ppm. The system then immediately switches on the nutrient 5 V submersible pumps with a rate of 2 LPM to supply adequate amounts at the right time.

The amount of nutrient solution needed

(11) $$=\mathrm{M}\mathrm{A}\mathrm{X}\mathrm{F}\mathrm{L}\mathrm{O}{\mathrm{W}}_{\mathrm{p}\mathrm{p}\mathrm{m}}-\mathrm{S}\mathrm{U}{\mathrm{R}}_{\mathrm{p}\mathrm{p}\mathrm{m}}$$

$$=2500-1700$$

$=800\mathrm{p}\mathrm{p}\mathrm{m}(\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{s}800\mathrm{m}\mathrm{g}/\mathrm{L}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r})$

Then the time needed to keep the pumps ON.

(12) $$={\displaystyle \frac{15Liter\times 800mg/Liter}{2\times {10}^{6}mg/Minute}}$$

(Sub in Eq. (11))

$=0.36sec(1\mathrm{L}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}=1000000\mathrm{m}\mathrm{g})$

Data analysis for nutrient supply

During the system implementation period, it was observed that the plants were taking nutrients at increasing levels as they were growing from one stage to another. We used Tomato plants for the demo and were kept in observation for around 115 days from the installation. With a view of data downloaded from the cloud server, we have clearly shown the average nutrient consumption per week in Table 2 and Figs. 5–7.

The following graph analysis developed using Python with the Matplotlib Library clearly shows how plant nutrient consumption rate increase with change in the growth stages.

Accuracy analysis chart for comparing the proposed with the existing system

Figure 8 and Table 3 compare the accuracy of the proposed methodology to various current methods. The graph shows that the deep learning approach improves performance and accuracy. For example, in the 1–5th week, the proposed model has a 97.5% accuracy value, while the CNN (Gul & Bora, 2023) and DNN (Arvind et al., 2020) models have 95.5% and 94.3% accuracy values, respectively. The proposed model, on the other hand, fared better with varied weeks. Similarly, the proposed model has an accuracy value of 99.4% under 10–15 weeks, whereas CNN and DNN have 96.8% and 96.6%, respectively.

Time complexity analysis of chart for comparing the proposed with the existing system

Figure 9 and Table 4 show the time complexity of the proposed methodology is compared to that of existing techniques. The data clearly shows that the proposed technique outperformed all other strategies. The proposed approach, for example, took only 123.23 ms to with vegetative stage, whereas other existing methods such as CNN and DNN have taken 319.24 and 233.83 ms, respectively. Likewise, the proposed approach takes 152.82 ms with flower stage, while existing techniques like CNN and DNN take 362.84, and 263.73 ms, respectively. Similarly, the proposed approach takes 182.54 ms with fruit stage, while existing techniques like CNN and DNN take 382.64, and 293.64 ms, respectively.